DIMPLE PATTERNS FOR GOLF BALLS

Abstract

The present invention provides dimple patterns with icosahedral tilings where the dimples are arranged in multiple copies of a first domain and a second domain, and the dimple pattern in the first domain is different than the dimple pattern in the second domain. A majority of dimples are provided having a first plan shape and a first profile shape, and at least one of the domains has a sub-pattern of nearest neighbor dimples having either a plan shape or a dimple profile shape that is different than the majority of dimples.

Claims

1. A golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, and the dimple pattern in the first domain is different than the dimple pattern in the second domain, wherein the first domain and the second domain are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting of twenty first domains and twelve second domains, and wherein, a majority of dimples have a first plan shape and a first profile shape, and wherein at least one of the domains has a sub-pattern of nearest neighbor dimples having either a plan shape or a dimple profile shape that is different than the majority of dimples.

2. The golf ball of claim 1, wherein the first domain has three-way rotational symmetry about a central point of the first domain and the second domain has five-way rotational symmetry about a central point of the second domain.

3. The golf ball of claim 2, wherein the sub-pattern of nearest neighbor dimples are axially symmetric about the central point of one of the two domains.

4. The golf ball of claim 2, wherein the sub-pattern of nearest neighbor dimples have a different plan shape than the majority of dimples.

5. The golf ball of claim 4, wherein the majority of dimples have a continuous plan shape and the sub-pattern dimples have a plan shape that is discontinuous.

6. The golf ball of claim 4, wherein the majority of dimples have a circular plan shape.

7. The golf ball of claim 6, wherein the sub-pattern of dimples have a polygonal plan shape.

8. The golf ball of claim 6, wherein the sub-pattern of dimples have plan shapes based on periodic functions along a path.

9. The golf ball of claim 6, wherein the sub-pattern of dimples have plan shapes made of circular arcs derived from polygons.

10. The golf ball of claim 2, wherein the sub-pattern of nearest neighbor dimples have a different dimple profile shape than the majority of dimples.

11. The golf ball of claim 10, wherein the majority of the dimples and the sub-pattern of dimples have different dimple profiles and are chosen from the group of spherical, conical, catenary, and Gabriel's horn.

12. The golf ball of claim 10, wherein the majority of dimples are spherical.

13. The golf ball of claim 12, wherein the sub-pattern of dimples are conical.

14. The golf ball of claim 12, wherein the sub-pattern of dimples are catenary.

15. The golf ball of claim 12, wherein the sub-pattern of dimples are chosen from the group of circumscribed prismatoids, rotational protrusions, frequency dimples, superposition dimples, Gabriel's horn dimples, or grooved dimple profiles.

16. The golf ball of claim 2, wherein the sub-pattern of dimples are all classified as interior dimples within a domain.

17. The golf ball of claim 16, wherein all of the interior dimples in one domain are sub-pattern dimples.

18. The golf ball of claim 1, wherein the sub-pattern of dimples are all classified as perimeter dimples within a domain.

19. The golf ball of claim 18, wherein all of the perimeter dimples of one domain are sub-pattern dimples.

20. The golf ball of claim 2, wherein the sub-pattern of dimples are both interior dimples and perimeter dimples within a domain.

21. The golf ball of claim 20, wherein the sub-pattern dimples are classified as perimeter dimples from the first domain and perimeter dimples from the second domain.

22. The golf ball of claim 2, wherein at least one sub-pattern dimple is at the center of one domain.

23. The golf ball of claim 22, wherein there is a sub-pattern dimple at the center of both domains.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In the accompanying drawings which form a part of the specification and are to be read in conjunction therewith and in which like reference numerals are used to indicate like parts in the various views:

[0028] FIG. 1A illustrates a golf ball having dimples arranged by a method of the invention; FIG. 1B illustrates a polyhedron face; FIG. 1C illustrates an element of the invention in the polyhedron face of FIG. 1B; and FIG. 1D illustrates a domain formed by a methods of the invention packed with dimples and formed from two elements of FIG. 1C;

[0029] FIG. 2 illustrates a single face of a polyhedron having control points thereon;

[0030] FIG. 3A illustrates a polyhedron face; FIG. 3B illustrates an element of the invention packed with dimples; FIG. 3C illustrates a domain of the invention packed with dimples formed from elements of FIG. 3B; and FIG. 3D illustrates a golf ball formed by a method of the invention formed of the domain of FIG. 3C;

[0031] FIG. 4A illustrates two polyhedron faces; FIG. 4B illustrates a first domain of the invention in the two polyhedron faces of FIG. 4A; FIG. 4C illustrates a first domain and a second domain of the invention in three polyhedron faces; FIG. 4D illustrates a golf ball formed by a method of the invention formed of the domains of FIG. 4C;

[0032] FIG. 5A illustrates a polyhedron face; FIG. 5B illustrates a first domain of the invention in a polyhedron face; FIG. 5C illustrates a first domain and a second domain of the invention in three polyhedron faces; and FIG. 5D illustrates a golf ball formed using a method of the invention formed of the domains of FIG. 5C;

[0033] FIG. 6A illustrates a polyhedron face; FIG. 6B illustrates a portion of a domain of the invention in the polyhedron face of FIG. 6A; FIG. 6C illustrates a domain formed by the methods of the invention; and FIG. 6D illustrates a golf ball formed using the methods of the invention formed of domains of FIG. 6C;

[0034] FIG. 7A illustrates a polyhedron face; FIG. 7B illustrates a domain of the invention in the polyhedron face of FIG. 7A; and FIG. 7C illustrates a golf ball formed by a method of the invention;

[0035] FIG. 8A illustrates a first element of the invention in a polyhedron face; FIG. 8B illustrates a first and a second element of the invention in the polyhedron face of FIG. 8A; FIG. 8C illustrates two domains of the invention composed of first and second elements of FIG. 8B; FIG. 8D illustrates a single domain of the invention based on the two domains of FIG. 8C; and FIG. 8E illustrates a golf ball formed using a method of the invention formed of the domains of FIG. 8D;

[0036] FIG. 9A illustrates a polyhedron face; FIG. 9B illustrates an element of the invention in the polyhedron face of FIG. 9A; FIG. 9C illustrates two elements of FIG. 9B combining to form a domain of the invention; FIG. 9D illustrates a domain formed by the methods of the invention based on the elements of FIG. 9C; and FIG. 9E illustrates a golf ball formed using a method formed of domains of FIG. 9D;

[0037] FIG. 10A illustrates a face of a rhombic dodecahedron; FIG. 10B illustrates a segment of the present invention in the face of FIG. 10A; FIG. 10C illustrates the segment of FIG. 10B and copies thereof forming a domain of the present invention; FIG. 10D illustrates a domain formed by a method of the present invention based on the segments of FIG. 10C; and FIG. 10E illustrates a golf ball formed by a method of the present invention formed of domains of FIG. 10D;

[0038] FIG. 11A utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

[0039] FIG. 11B utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

[0040] FIG. 11C depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

[0041] FIG. 11D depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of another of the irregular domains;

[0042] FIG. 11E shows the domains of FIG. 11C and FIG. 11D tessellated around a golf ball sphere;

[0043] FIG. 12A utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

[0044] FIG. 12B depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

[0045] FIG. 12C shows the domains of FIG. 12B tessellated around a golf ball sphere;

[0046] FIG. 13A depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

[0047] FIG. 13B shows the domains of FIG. 13A tessellated around a golf ball sphere;

[0048] FIG. 14A depicts first and second domains of the present invention; FIG. 14B depicts a majority of dimples and sub-pattern dimples in the first and second domains of the present invention; FIG. 14C illustrates a golf ball having the first and second domains of FIG. 14B tessellated on the surface of the golf ball; FIG. 14D depicts the cross-section of the majority of dimples showing the dimple profile; and FIG. 14E depicts the cross-section of the sub-pattern dimples showing the dimple profile;

[0049] FIG. 15A depicts first and second domains of the present invention; FIG. 15B depicts a majority of dimples and sub-pattern dimples in the first and second domains of the present invention; FIG. 15C illustrates a golf ball having the first and second domains of FIG. 15B tessellated on the surface of the golf ball; FIG. 15D depicts the cross-section of the majority of dimples showing the dimple profile; and FIG. 15E depicts the cross-section of the sub-pattern dimples showing the dimple profile; and

[0050] FIG. 16A depicts first and second domains of an embodiment of the present invention; FIG. 16B depicts a majority of dimples and sub-pattern dimples in the first and second domains of the present invention; FIG. 16C illustrates a golf ball having the first and second domains of FIG. 16B tessellated on the surface of the golf ball; FIG. 16D depicts the plan shape of the majority of dimples; and FIG. 16E depicts the plan shape of the sub-pattern dimples.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0051] The present invention provides a method for arranging dimples on a golf ball surface in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron. In the invention as described below extends the method of spherical tiling to include sub-patterns of dimples within the base geometry dimple packing. Unique patterns are thus created with improved aerodynamics and visual aesthetics.

[0052] In one embodiment, illustrated in FIG. 1A, the present invention comprises a golf ball 10 comprising dimples 12. Dimples 12 are arranged by packing irregular domains 14 with dimples, as seen best in FIG. 1D. Irregular domains 14 are created in such a way that, when tessellated on the surface of golf ball 10, they impart greater orders of symmetry to the surface than prior art balls. The irregular shape of domains 14 additionally minimize the appearance and effect of the golf ball parting line from the molding process, and allows greater flexibility in arranging dimples than would be available with regularly shaped domains.

[0053] The irregular domains can be defined through the use of any one of the exemplary methods described herein. Each method produces one or more unique domains based on circumscribing a sphere with the vertices of a regular polyhedron. The vertices of the circumscribed sphere based on the vertices of the corresponding polyhedron with origin (0,0,0) are defined below in Table 1.

TABLE-US-00001 TABLE 1 Vertices of Circumscribed Sphere based on Corresponding Polyhedron Vertices Type of Polyhedron Vertices Tetrahedron (+1, +1, +1); (−1, −1, +1); (−1, +1, −1); (+1, −1, −1) Cube (±1, ±1, ±1) Octahedron (±1, 0, 0); (0, ±1, 0); (0, 0, ±1) Dodecahedron (±1, ±1, ±1); (0, ±1/φ, ±φ); (±1/φ, ±φ, 0); (±φ, 0, ±1/φ)* Icosahedron (0, ±1, ±φ); (±1, ±φ, 0); (±φ, 0, ±1)* *φ = (1 + {square root over (5)})/2

[0054] Each method has a unique set of rules which are followed for the domain to be symmetrically patterned on the surface of the golf ball. Each method is defined by the combination of at least two control points. These control points, which are taken from one or more faces of a regular or non-regular polyhedron, consist of at least three different types: the center C of a polyhedron face; a vertex V of a face of a regular polyhedron; and the midpoint M of an edge of a face of the polyhedron. FIG. 2 shows an exemplary face 16 of a polyhedron (a regular dodecahedron in this case) and one of each a center C, a midpoint M, a vertex V, and an edge E on face 16.

[0055] The two control points C, M, or V may be of the same or different types. Accordingly, six types of methods for use with regular polyhedrons are defined as follows:

[0056] 1. Center to midpoint (C.fwdarw.M);

[0057] 2. Center to center (C.fwdarw.C);

[0058] 3. Center to vertex (C.fwdarw.V);

[0059] 4. Midpoint to midpoint (M.fwdarw.M);

[0060] 5. Midpoint to Vertex (M.fwdarw.V); and

[0061] 6. Vertex to Vertex (V.fwdarw.V).

[0062] While each method differs in its particulars, they all follow the same basic scheme. First, a non-linear sketch line is drawn connecting the two control points. This sketch line may have any shape, including, but not limited, to an arc, a spline, two or more straight or acute lines or curves, or a combination thereof. Second, the sketch line is patterned in a method specific manner to create a domain, as discussed below. Third, when necessary, the sketch line is patterned in a second fashion to create a second domain.

[0063] While the basic scheme is consistent for each of the six methods, each method preferably follows different steps in order to generate the domains from a sketch line between the two control points, as described below with reference to each of the methods individually.

The Center to Vertex Method

[0064] Referring again to FIGS. 1A-1D, the center to vertex method yields a domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows: [0065] 1. A regular polyhedron is chosen (FIGS. 1A-1D use an icosahedron); [0066] 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 1B; [0067] 3. Center C of face 16, and a first vertex V.sub.1 of face 16 are connected with any non-linear sketch line, hereinafter referred to as a segment 18; [0068] 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with vertex V.sub.2 adjacent to vertex V.sub.1. The two segments 18 and 20 and the edge E connecting vertices V.sub.1 and V.sub.2 define an element 22, as shown best in FIG. 1C; and [0069] 5. Element 22 is rotated about midpoint M of edge E to create a domain 14, as shown best in FIG. 1D.

[0070] When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 1A, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and V.sub.1. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P.sub.F of the polyhedron chosen times the number of edges P.sub.E per face of the polyhedron divided by 2, as shown below in Table 2.

[0071] TABLE 2: Domains Resulting from Use of Specific Polyhedra when Using the

TABLE-US-00002 TABLE 2 Domains Resulting Form Use of Specific Polyhedra When Using the Center to Vertex Method Type of Number of Faces, Number Number of Domains Polyhedron P.sub.F of Edges, P.sub.E 14 Tetrahedron 4 3 6 Cube 6 4 12 Octahedron 8 3 12 Dodecahedron 12 5 30 Icosahedron 20 3 30

The Center to Midpoint Method

[0072] Referring to FIGS. 3A-3D, the center to midpoint method yields a single irregular domain that can be tessellated to cover the surface of golf ball 10. The domain is defined as follows:

[0073] 1. A regular polyhedron is chosen (FIGS. 3A-3D use a dodecahedron);

[0074] 2. A single face 16 of the regular polyhedron is chosen, shown in FIG. 3A;

[0075] 3. Center C of face 16, and midpoint M.sub.1 of a first edge E.sub.1 of face 16 are connected with a segment 18;

[0076] 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M.sub.2 of a second edge E.sub.2 adjacent to first edge E.sub.1. The two segments 16 and 18 and the portions of edge E.sub.1 and edge E.sub.2 between midpoints M.sub.1 and M.sub.2 define an element 22; and

[0077] 5. Element 22 is patterned about vertex V of face 16 which is contained in element 22 and connects edges E.sub.1 and E.sub.2 to create a domain 14.

[0078] When domain 14 is tessellated around a golf ball 10 to cover the surface of golf ball 10, as shown in FIG. 3D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and M.sub.1. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of vertices P.sub.v of the chosen polyhedron, as shown below in Table 3.

TABLE-US-00003 TABLE 3 Domains resulting from use of specific Polyhedra when using the Center to Midpoint Method Type of Polyhedron Number of Vertices, P.sub.V Number of Domains 14 Tetrahedron 4 4 Cube 8 8 Octahedron 6 6 Dodecahedron 20 20 Icosahedron 12 12

The Center to Center Method

[0079] Referring to FIGS. 4A-4D, the center to center method yields two domains that can be tessellated to cover the surface of golf ball 10. The domains are defined as follows: [0080] 1. A regular polyhedron is chosen (FIGS. 4A-4D use a dodecahedron); [0081] 2. Two adjacent faces 16a and 16b of the regular polyhedron are chosen, as shown in FIG. 4A; [0082] 3. Center C.sub.1 of face 16a, and center C.sub.2 of face 16b are connected with a segment 18; [0083] 4. A copy 20 of segment 18 is rotated 180 degrees about the midpoint M between centers C.sub.1 and C.sub.2, such that copy 20 also connects center C.sub.1 with center C.sub.2, as shown in FIG. 4B. The two segments 16 and 18 define a first domain 14a; and [0084] 5. Segment 18 is rotated equally about vertex V to define a second domain 14b, as shown in FIG. 4C.

[0085] When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in FIG. 4D, a different number of total domains 14a and 14b will result depending on the regular polyhedron chosen as the basis for control points C.sub.1 and C.sub.2. The number of first and second domains 14a and 14b used to cover the surface of golf ball 10 is P.sub.F*P.sub.E/2 for first domain 14a and P.sub.v for second domain 14b, as shown below in Table 4.

TABLE-US-00004 TABLE 4 Domains Resulting From Use of Specific Polyhedra When Using the Center to Center Method Number of Number Number of Number of First of Second Type of Vertices, Domains Faces, Number of Domains Polyhedron P.sub.V 14a P.sub.F Edges, P.sub.E 14b Tetrahedron 4 6 4 3 4 Cube 8 12 6 4 8 Octahedron 6 9 8 3 6 Dodecahedron 20 30 12 5 20 Icosahedron 12 18 20 3 12

The Midpoint to Midpoint Method

[0086] Referring to FIGS. 5A-5D, the midpoint to midpoint method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows: [0087] 1. A regular polyhedron is chosen (FIGS. 5A-5D use a dodecahedron); [0088] 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 5A; [0089] 3. The midpoint M.sub.1 of a first edge E.sub.1 of face 16, and the midpoint M.sub.2 of a second edge E.sub.2 adjacent to first edge E.sub.1 are connected with a segment 18; [0090] 4. Segment 18 is patterned around center C of face 16 to form a first domain 14a, as shown in FIG. 5B; [0091] 5. Segment 18, along with the portions of first edge E.sub.1 and second edge E.sub.2 between midpoints M.sub.1 and M.sub.2, define an element 22; and [0092] 6. Element 22 is patterned about vertex V which is contained in element 22 and connects edges E.sub.1 and E.sub.2 to create a second domain 14b, as shown in FIG. 5C.

[0093] When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in FIG. 5D, a different number of total domains 14a and 14b will result depending on the regular polyhedron chosen as the basis for control points M.sub.1 and M.sub.2. The number of first and second domains 14a and 14b used to cover the surface of golf ball 10 is P.sub.F for first domain 14a and P.sub.v for second domain 14b, as shown below in Table 5.

TABLE-US-00005 TABLE 5 Domains resulting from use of specific polyhedra when using the Center to Center Method Number Number of Number of Type of Number of of First Vertices, Second Domains Polyhedron Faces, P.sub.F Domains 14a P.sub.V 14b Tetrahedron 4 4 4 4 Cube 6 6 8 8 Octahedron 8 8 6 6 Dodecahedron 12 12 20 20 Icosahedron 20 20 12 12

The Midpoint to Vertex Method

[0094] Referring to FIGS. 6A-6D, the midpoint to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows: [0095] 1. A regular polyhedron is chosen (FIGS. 6A-6D use a dodecahedron); [0096] 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 6A; [0097] 3. A midpoint M.sub.1 of edge E.sub.1 of face 16 and a vertex V.sub.1 on edge E.sub.1 are connected with a segment 18; [0098] 4. Copies 20 of segment 18 is patterned about center C of face 16, one for each midpoint M.sub.2 and vertex V.sub.2 of face 16, to define a portion of domain 14, as shown in FIG. 6B; and [0099] 5. Segment 18 and copies 20 are then each rotated 180 degrees about their respective midpoints to complete domain 14, as shown in FIG. 6C.

[0100] When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 6D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M.sub.1 and V.sub.1. The number of domains 14 used to cover the surface of golf ball 10 is P.sub.F, as shown in Table 6.

TABLE-US-00006 TABLE 6 Domains resulting from use of specific polyhedra when using the Midpoint to Vertex Method Type of Polyhedron Number of Faces, P.sub.F Number of Domains 14 Tetrahedron 4 4 Cube 6 6 Octahedron 8 8 Dodecahedron 12 12 Icosahedron 20 20

The Vertex to Vertex Method

[0101] Referring to FIGS. 7A-7C, the vertex to vertex method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows: [0102] 1. A regular polyhedron is chosen (FIGS. 7A-7C use an icosahedron); [0103] 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 7A; [0104] 3. A first vertex V.sub.1 face 16, and a second vertex V.sub.2 adjacent to first vertex V.sub.1 are connected with a segment 18; [0105] 4. Segment 18 is patterned around center C of face 16 to form a first domain 14a, as shown in FIG. 7B; [0106] 5. Segment 18, along with edge E.sub.1 between vertices V.sub.1 and V.sub.2, defines an element 22; and [0107] 6. Element 22 is rotated around midpoint M.sub.1 of edge E.sub.1 to create a second domain 14b.

[0108] When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in FIG. 7C, a different number of total domains 14a and 14b will result depending on the regular polyhedron chosen as the basis for control points V.sub.1 and V.sub.2. The number of first and second domains 14a and 14b used to cover the surface of golf ball 10 is P.sub.F for first domain 14a and P.sub.F*P.sub.E/2 for second domain 14b, as shown below in Table 7.

TABLE-US-00007 TABLE 7 Domains resulting from use of specific polyhedra when using the Vertex to Vertex Method Number of Number Number of Second Type of Number of of First Edges per Face, Domains Polyhedron Faces, P.sub.F Domains 14a P.sub.E 14b Tetrahedron 4 4 3 6 Cube 6 6 4 12 Octahedron 8 8 3 12 Dodecahedron 12 12 5 30 Icosahedron 20 20 3 30

[0109] While the six methods previously described each make use of two control points, it is possible to create irregular domains based on more than two control points. For example, three, or even more, control points may be used. The use of additional control points allows for potentially different shapes for irregular domains. An exemplary method using a midpoint M, a center C and a vertex V as three control points for creating one irregular domain is described below.

The Midpoint to Center to Vertex Method

[0110] Referring to FIGS. 8A-8E, the midpoint to center to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows: [0111] 1. A regular polyhedron is chosen (FIGS. 8A-8E use an icosahedron); [0112] 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 8A; [0113] 3. A midpoint M.sub.1 on edge E.sub.1 of face 16, Center C of face 16 and a vertex V.sub.1 on edge E.sub.1 are connected with a segment 18, and segment 18 and the portion of edge E.sub.1 between midpoint M.sub.1 and vertex V.sub.1 define a first element 22a, as shown in FIG. 8A; [0114] 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M.sub.2 on edge E.sub.2 adjacent to edge E.sub.1, and connects center C with a vertex V.sub.2 at the intersection of edges E.sub.1 and E.sub.2, and the portion of segment 18 between midpoint M.sub.1 and center C, the portion of copy 20 between vertex V.sub.2 and center C, and the portion of edge E.sub.1 between midpoint M.sub.1 and vertex V.sub.2 define a second element 22b, as shown in FIG. 8B; [0115] 5. First element 22a and second element 22b are rotated about midpoint M.sub.1 of edge E.sub.1, as seen in FIG. 8C, to define two domains 14, wherein a single domain 14 is bounded solely by portions of segment 18 and copy 20 and the rotation 18′ of segment 18, as seen in FIG. 8D. When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 8E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M, C, and V. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P.sub.F of the polyhedron chosen times the number of edges P.sub.E per face of the polyhedron, as shown below in Table 8.

TABLE-US-00008 TABLE 8 Domains resulting from use of specific polyhedra when using the Midpoint to Center to Vertex Method Number Type of Number of Faces, of Domains Polyhedron P.sub.F Number of Edges, P.sub.E 14 Tetrahedron 4 3 12 Cube 6 4 24 Octahedron 8 3 24 Dodecahedron 12 5 60 Icosahedron 20 3 60

[0116] While the methods described previously provide a framework for the use of center C, vertex V, and midpoint M as the only control points, other control points are useable. For example, a control point may be any point P on an edge E of the chosen polyhedron face. When this type of control point is used, additional types of domains may be generated, though the mechanism for creating the irregular domain(s) may be different. An exemplary method, using a center C and a point P on an edge, for creating one such irregular domain is described below.

The Center to Edge Method

[0117] Referring to FIGS. 9A-9E, the center to edge method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows: [0118] 1. A regular polyhedron is chosen (FIGS. 9A-9E use an icosahedron); [0119] 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 9A; [0120] 3. Center C of face 16, and a point P.sub.1 on edge E.sub.1 are connected with a segment 18; [0121] 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a point P.sub.2 on edge E.sub.2 adjacent to edge E.sub.1, where point P.sub.2 is positioned identically relative to edge E.sub.2 as point P.sub.1 is positioned relative to edge E.sub.1, such that the two segments 18 and 20 and the portions of edges E.sub.1 and E.sub.2 between points P.sub.1 and P.sub.2, respectively, and a vertex V, which connects edges E.sub.1 and E.sub.2, define an element 22, as shown best in FIG. 9B; and [0122] 5. Element 22 is rotated about midpoint M.sub.1 of edge E.sub.1 or midpoint M.sub.2 of edge E.sub.2, whichever is located within element 22, as seen in FIGS. 9B-9C, to create a domain 14, as seen in FIG. 9D.

[0123] When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 9E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and P.sub.1. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P.sub.F of the polyhedron chosen times the number of edges P.sub.E per face of the polyhedron divided by 2, as shown below in Table 9.

TABLE-US-00009 TABLE 9 Domains resulting from use of specific polyhedra when using the Center to Edge Method Number Type of Number of Faces, of Domains Polyhedron P.sub.F Number of Edges, P.sub.E 14 Tetrahedron 4 3 6 Cube 6 4 12 Octahedron 8 3 12 Dodecahedron 12 5 30 Icosahedron 20 3 30

[0124] Though each of the above described methods has been explained with reference to regular polyhedrons, they may also be used with certain non-regular polyhedrons, such as Archimedean Solids, Catalan Solids, or others. The methods used to derive the irregular domains will generally require some modification in order to account for the non-regular face shapes of the non-regular solids. An exemplary method for use with a Catalan Solid, specifically a rhombic dodecahedron, is described below.

A Vertex to Vertex Method for a Rhombic Dodecahedron

[0125] Referring to FIGS. 10A-10E, a vertex to vertex method based on a rhombic dodecahedron yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows: [0126] 1. A single face 16 of the rhombic dodecahedron, as in FIG. 10A; [0127] 2. A first vertex V.sub.1 face 16, and a second vertex V.sub.2 adjacent to first vertex V.sub.1 are connected with a segment 18, as shown in FIG. 10B; [0128] 3. A first copy 20 of segment 18 is rotated about vertex V.sub.2, such that it connects vertex V.sub.2 to vertex V3 of face 16, a second copy 24 of segment 18 is rotated about center C, such that it connects vertex V.sub.3 and vertex V.sub.4 of face 16, and a third copy 26 of segment 18 is rotated about vertex V.sub.1 such that it connects vertex V.sub.1 to vertex V.sub.4, all as shown in FIG. 10C, to form a domain 14, as shown in FIG. 10D;

[0129] When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 10E, twelve domains will be used to cover the surface of golf ball 10, one for each face of the rhombic dodecahedron.

[0130] One additional embodiment to the above methods of spherical tiling extends these methods to include sub-patterns of dimples within the irregular domain(s) dimple packing 101. The method includes choosing a spherical tiling base geometry and tiling method, defining a sub-pattern of nearest neighbor dimples 102 within the irregular domain(s), and packing dimples within the remaining un-dimpled region. Until the present invention, arranging dimples on the surface of a golf ball has previously been done solely working within a segment of the desired dimple pattern geometry. The present invention is novel because a sub-pattern of nearest neighbor dimples is first defined on the blank spherical segment of the irregular domain(s). The remaining un-dimpled regions are then packed around the initial defining sub-pattern of nearest neighbor dimples. This can yield both aesthetic and aerodynamic performance advantages.

[0131] The process is started with a spherical section, which is circumscribed using the vertices of a regular polyhedron (as previously shown in Table 1), and it should be understood that any of the polyhedron types listed in Table 1 can be used. Illustrative examples, shown here consist of a tetrahedron and an icosahedron. Using the mid-point to mid-point tiling method and a tetrahedral base, the irregular domains 101 illustrated in FIG. 11A and FIG. 11B are created.

[0132] The dimple sub-pattern can be defined as nearest neighbor dimples on or within edges of one or more of the irregular domains. The sub-pattern 102 in the current example is defined within both irregular domains. Once the sub-pattern is defined, the remaining unpacked spherical region is packed around the initial sub-pattern of dimples as illustrated in FIG. 11C and FIG. 11D, wherein the sub-pattern dimples 102 are denoted by the gray color. Once the sub-pattern is defined and the remaining unpacked spherical region around the initial sub-pattern is packed with dimples, the dimpled spherical region may then be tessellated, as seen in the golf ball 100 shown in FIG. 11E. The sub-pattern dimples may be packed within any number of the irregular domains.

[0133] Although the dimple sub-pattern is defined by nearest neighbor dimples, each instance of the sub-pattern may or may not be continuously connected by sub-pattern nearest neighbor dimples around the ball surface after the domains are tessellated.

[0134] The method of determining nearest neighbor dimples is illustrated in FIG. 11C, wherein two tangency lines TL are drawn from the center of a first dimple to a potential nearest neighbor dimple. Additionally, a line segment Ls is drawn connecting the center of the first dimple to the center of the potential nearest neighbor dimple. If there is no line segment that is intersected by another dimple, or portion of a dimple, then those dimples are considered to be nearest neighbor dimples.

[0135] Additional examples use an icosahedron as the base pattern and the midpoint to midpoint method to create two irregular domains 101 in FIG. 12A. A sub-pattern of dimples 102 are defined within a single domain in, FIG. 12B and FIG. 13A, and additional dimples are defined within the unpacked region of the irregular domains. The irregular domains are tessellated to create a golf ball 100 with a sub-pattern that is connected throughout the tessellation (FIG. 13B) and a golf ball 100 with a sub-pattern that is disconnected throughout the tessellation (FIG. 12C).

[0136] Visual distinction may be achieved between the sub-pattern dimples and the remaining dimples, by exhibiting the sub-pattern dimples with one or more of the following characteristics: different perimeter shape; dimple profile; color; texture; grooves; or brambles. Also, the dimples packing the remaining spherical region, which is defined by the existing dimple sub-pattern, may have different perimeter shape, dimple profile, color, or texture.

[0137] Dimples with circular perimeters should have diameters that fall within the range of 0.100 to 0.220 inches. Dimples with non-circular perimeters should be circumscribed by a circle with a diameter that falls within the range of 0.120 to 0.270 inches.

[0138] Each irregular domain preferably contains between 10 and 115 dimples, and the nearest initial sub-pattern of nearest neighbor dimples preferably contains between 2 and 80 dimples.

[0139] Preferred high performance golf balls will usually have a staggered parting line that passes through the section and normally intersects two edges of the section.

[0140] The surface coverage of the dimples on the golf ball should be between 70 to 90%, while the surface coverage of the nearest neighbor sub-pattern of dimples should be between 10% and 60%.

[0141] Dimples may exhibit a contrasting color(s); the perimeter shape may be circular, polygonal, or elliptical. Dimple profiles can include, but are not limited to, spherical, Gabriel's horn, catenary, conical, Witch of Agnesi, chalice, elliptical, superposition of two curves, or any other spherically weighted profile.

[0142] There are no limitations on how the dimples are packed. There are likewise no limitations to the dimple shapes or profiles selected to pack the domains. Though the present invention includes substantially circular dimples in one embodiment, dimples or protrusions (brambles) having any desired characteristics and/or properties may be used. For example, in one embodiment the dimples may have a variety of shapes and sizes including different depths and widths. In particular, the dimples may be concave hemispheres, or they may be triangular, square, hexagonal, catenary, polygonal or any other shape known to those skilled in the art. They may also have straight, curved, or sloped edges or sides. Any type of dimple or protrusion (bramble) known to those skilled in the art may be used with the present invention. Alternatively, the tessellation can create a pattern that covers more than about 60%, preferably more than about 70% and preferably more than about 80% of the golf ball surface.

[0143] In other embodiments, the domains may not be packed with dimples, and the borders of the irregular domains may instead comprise ridges or channels. In golf balls having this type of irregular domain, the one or more domains or sets of domains preferably overlap to increase surface coverage of the channels.

[0144] When the domain(s) is patterned onto the surface of a golf ball, the arrangement of the domains dictated by their shape and the underlying polyhedron ensures that the resulting golf ball has a high order of symmetry, equaling or exceeding 12. The order of symmetry of a golf ball produced using the method of the current invention will depend on the regular or non-regular polygon on which the irregular domain is based. The order and type of symmetry for golf balls produced based on the five regular polyhedra are listed below in Table 10.

TABLE-US-00010 TABLE 10 Symmetry of Golf Ball of the Present Invention as a Function of Polyhedron Type of Polyhedron Type of Symmetry Symmetrical Order Tetrahedron Chiral Tetrahedral Symmetry 12 Cube Chiral Octahedral Symmetry 24 Octahedron Chiral Octahedral Symmetry 24 Dodecahedron Chiral Icosahedral Symmetry 60 Icosahedron Chiral Icosahedral Symmetry 60

[0145] The benefits of these high orders of symmetry include more even dimple distribution, the potential for higher packing efficiency, and improved means to mask the ball parting line. Further, dimple patterns generated in this manner may have improved flight stability and symmetry as a result of the higher degrees of symmetry.

[0146] In other embodiments, the irregular domains do not completely cover the surface of the ball, and there are open spaces between domains that may or may not be filled with dimples. This allows dissymmetry to be incorporated into the ball.

[0147] In another embodiment, the present invention is directed to dimple patterns based on icosahedral tilings. Isocsahedral tiling is specifically described in U.S. Pat. No. 9,504,877, the entire disclosure of which is hereby incorporated herein by reference in its entirety. The dimple pattern of the present embodiment is arranged in two irregular domains as described in U.S. Pat. No. 9,468,810 and U.S. application Ser. No. 15/263,408, the entire disclosures of which are hereby incorporated herein by reference in their entirety. The preferred icosahedron pattern of the present invention consists of twenty irregular first domains and twelve irregular second domains. Preferably, the first and second irregular domains are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles. The dimples within the irregular domains consist of a first dimple type that makes up the majority of the dimples on the golf ball and a second dimple type that is different from the first dimple type and constitutes a sub-pattern of nearest neighbor dimples within the irregular domains.

[0148] The sub-pattern dimples, or second dimple type, are different in either dimple profile shape and/or in dimple plan shape (i.e. perimeter shape). The sub-pattern of dimples preferably has more than one dimple.

[0149] Dimple profiles of either the majority dimples (first dimple type) or the sub-pattern of dimples (second dimple type) may be selected from the group of: spherical dimples, conical dimples as described in U.S. Pat. Nos. 8,137,217, 8,632,426 and 9,220,945 the entire disclosures of which are hereby incorporated herein by reference in their entirety, dimples with rotational protrusions as described in U.S. Pat. No. 8,353,789 the entire disclosure of which is hereby incorporated herein by reference in its entirety, circumscribed prismatoids as described in U.S. Pat. Nos. 8,926,453 and 8,317,638 the entire disclosures of which are hereby incorporated herein by reference in their entirety, frequency dimples or Witch of Agnesi curve dimples as described in U.S. Publ. No. 2012/0122613 the entire disclosure of which is hereby incorporated herein by reference in its entirety, catenary dimples as described in U.S. Pat. Nos. 7,887,439, 7,641,572, 7,163,472 and 6,796,912 the entire disclosures of which are hereby incorporated herein by reference in their entirety, superposition dimples as described in U.S. Publ. Nos. 2016/0279478, 2016/0129314 and 2015/0119171 the entire disclosures of which are hereby incorporated herein by reference in their entirety, Gabriel's horn dimples as described in U.S. Publ. No. 2013/0172124 the entire disclosure of which is hereby incorporated herein by reference in its entirety, and grooved dimples as described in U.S. Publ. No. 2014/0135146 the entire disclosure of which is hereby incorporated herein by reference in its entirety.

[0150] Dimple plan shapes of either the majority dimples (first dimple types) or the sub-pattern of dimples (second dimple types) may be selected from one of: circular, polygonal, periodic functions along a path as described in U.S. patent application Ser. Nos. 14/941,841, 14/948,251 and 14/948,252 the entire disclosures of which are hereby incorporated herein by reference in their entirety, circular arcs derived from polygons as described in U.S. patent application Ser. No. 14/941,916 the entire disclosure of which is hereby incorporated herein by reference in its entirety, and irregularly shaped dimples.

[0151] For purposes of the embodiments described in FIGS. 14-16 of the present disclosure, each dimple on the outer surface of the golf ball is either a perimeter dimple or an interior dimple and is positioned entirely within either an irregular first domain or an irregular second domain. Perimeter dimples are those dimples located directly adjacent to a border segment. The perimeter dimples of a given irregular domain are those located inside of that domain, and, in a particular embodiment, form an axially symmetric pattern about the geometric center of the domain. Interior dimples are those dimples not located directly adjacent to a border segment. The interior dimples of a given irregular domain are those located within the domain, and, in a particular embodiment, form an axially symmetric pattern about the geometric center of the domain. Perimeter and interior dimples are described in greater detail in U.S. patent application Ser. No. 15/242,217, the entire disclosure of which is hereby incorporated herein by reference in its entirety.

[0152] A specific embodiment is shown in FIGS. 14A-E. This embodiment is a spherical tiling based on an icosahedron pattern having a first domain 200 and a second domain 202. The dimple pattern within each domain is axially symmetric about a center of the domain C.sub.1 and C.sub.2. The first domain 200 and second domain 202 are tessellated to cover the outer surface of the golf ball 208 in a uniform pattern having no great circles and consisting of twenty first domains 200 and twelve second domains 202. The iscosahedron pattern consists of a majority of dimples 204 of a first dimple type and sub-pattern dimples 206 of a second dimple type. As shown in FIGS. 14A-E, the majority of dimples 204 are shown as unshaded while the sub-pattern dimples 206 are identified as the shaded dimples. In this particular example, the majority dimples 204 have a spherical dimple profile as shown in FIG. 14D and a circular plan shape as shown in FIGS. 14A-C, and the sub-pattern dimples 206 have a conical dimple profile as shown in FIG. 14E and a circular plan shape as shown in FIGS. 14A-C. As shown in FIGS. 14A-C, sub-pattern dimples 206 are all perimeter dimples in the first domain 200 and have 3-way axial symmetry about the center C.sub.1 of the first domain 200.

[0153] Referring now to the specific embodiment of FIGS. 15A-E, this embodiment is a spherical tiling based on an icosahedron pattern with a first domain 300 and a second domain 302. The dimple pattern within each domain is axially symmetric about a center of the domain C.sub.1 and C.sub.2. The first domain 300 and second domain 302 are tessellated to cover the outer surface of the golf ball 308 in a uniform pattern having no great circles and consisting of twenty first domains 300 and twelve second domains 302. The iscosahedron pattern consists of the majority dimples 304 of a first dimple type and the sub-pattern dimples 306 of a second dimple type. As shown in FIGS. 15A-C, the majority of dimples 304 are shown as unshaded while the sub-pattern dimples 306 are identified as the shaded dimples. In this particular example, the majority dimples 304 have a catenary dimple profile as shown in FIG. 15D and a circular plan shape as shown in FIG. 15A-C, and the sub-pattern dimples 306 have a dimple profile in the shape of a Gabriel's horn as shown in FIG. 15E and a circular plan shape as shown in FIGS. 15A-C. As is apparent from FIGS. 15A-C, the sub-pattern dimples 306 are both perimeter dimples and interior dimples in the second domain 302 and are 5-way axially symmetric about the center C.sub.2 of the second domain 302.

[0154] Referring now to the specific embodiment of FIGS. 16A-E, this embodiment is a spherical tiling based on an icosahedron pattern with a first domain 400 and a second domain 402. The dimple pattern within each domain is axially symmetric about the center of the domain C.sub.1 and C.sub.2. The first domain 400 and second domain 402 are tessellated to cover the outer surface of the golf ball 408 in a uniform pattern having no great circles and consisting of twenty first domains 400 and twelve second domains 402. The iscosahedron pattern consists of the majority dimples 404 of a first dimple type and the sub-pattern dimples 406 of a second dimple type. As shown in FIGS. 16A-C, the majority of dimples 404 are shown as unshaded while the sub-pattern dimples 406 are identified as the shaded dimples. In this particular example, the majority dimples 404 have a circular plan shape as shown in FIGS. 16A-D, and the sub-pattern dimples 406 have a discontinuous plan shape using circular arcs as shown in FIGS. 16A-C and E. It is apparent that the sub-pattern dimples 406 are perimeter dimples of the second domain 402 and have five-way axial symmetry about the center C.sub.2 of the second domain 402.

[0155] The preferred dimple coverage of the present invention is greater than 75%, or more preferably 80% or more preferably 85%. Preferably, dimple counts for the present invention range from about 200 to about 500 dimples and more preferably from about 300 to about 400 dimples. Preferably, dimples sizes for the present invention range from about 0.10 to about 0.22 inches, more preferably from about 0.12 to about 0.2 inches and most preferably from about 0.125 to about 0.195 inches. As will be appreciated from the drawings, the majority of dimples (first dimple type) and sub-pattern dimples (second dimple type) may include dimples of different sizes.

[0156] While the preferred embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not of limitation. It will be apparent to persons skilled in the relevant art that various changes in form and detail can be made therein without departing from the spirit and scope of the invention. For example, while the preferred polyhedral shapes have been provided above, other polyhedral shapes could also be used. Thus the present invention should not be limited by the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.