A honeycomb filter includes a pillar-shaped honeycomb structure body having a porous partition wall disposed, surrounding a plurality of cells which serve as fluid through channels extending from a first end face to a second end face; and a plugging portion provided at an open end on the first end face side or the second end face side of each of the cells, wherein the partition wall is composed of a material containing cordierite as a main component thereof, an average pore diameter of the partition wall is 20 to 30 μm, an average equivalent circle diameter of pores existing at a surface of the partition wall and having equivalent circle diameters exceeding 3.0 μm is 18 to 30 μm, and a number per unit area of pores existing at a surface of the partition wall and having equivalent circle diameters exceeding 3.0 μm is 400 per mm.sup.2 or more.

A honeycomb structure includes a pillar-shaped honeycomb structure body having porous partition walls surrounding a plurality of cells which extend from a first to a second end face and which form flow channels of a fluid, and a circumferential wall enclosing the partition walls, wherein, specific cell of the cells is provided with a pair of projection which projects into the cell from the partition wall, the projection projects, in at least a pair of opposed partition walls among the partition walls constituting the cell, into the cell from a first and a second side, and which is provided continuously in a direction the cell extends, and in the case where the width of a top part of the projection is denoted by W1, and the width of a bottom part of the projection is denoted by W2, W1>W2 holds, and W2/W1 is 0.5 to 0.9.

A pillar shaped honeycomb structure includes: a porous partition wall that defines a plurality of cells, the cells forming flow paths for a fluid, the cells extending from an inflow end face to an outflow end face; and an outer peripheral wall located at the outermost circumference. At least a part of surfaces of the partition walls has a surface layer, and the surface layer includes magnetic particles and has permeability.

A honeycomb filter includes a pillar-shaped honeycomb structure having porous partition walls placed, surrounding a plurality of cells which serve as fluid through channels extending from an inflow end face to an outflow end face; and porous plugging portions provided either at the ends on the inflow end face side of the cells or at the ends on the outflow end face side of the cells, wherein the plugging portions include plugging portions that have voids therein, and in the plugging portions having the voids, porosity including the voids as pores ranges from 68% to 83%.

A honeycomb filter includes a pillar-shaped honeycomb structure having porous partition walls provided, surrounding a plurality of cells which serve as fluid through channels extending from an inflow end face to an outflow end face, and porous plugging portions provided either at the ends on the inflow end face side or the outflow end face side of the cells, wherein the plugging portions are composed of a porous material, the honeycomb structure has a central region and a circumferential region, and a ratio of an area of the circumferential region with respect to that of the central region ranges from 0.1 to 0.5, porosity of a central plugging portion in the central region, is higher than that of a circumferential plugging portion in the circumferential region, and the porosity of the central plugging portion ranges from 76% to 85%, and that of the circumferential plugging portion from 60% to 75%.

A honeycomb structure, including: a honeycomb structure body having a porous partition walls which are disposed to define a plurality of cells and a circumferential wall, wherein the partition walls are provided with protrusions which protrude to extend into the cells and are continuously disposed in an extending direction of the cells, the cells have a polygonal shape in a cross section orthogonal to the extending direction of the cells, the plurality of cells include a plurality of specific cells having at least one place where two sides each of which is provided with a different number of protrusions intersect each other, and in the cross section orthogonal to the extending direction of the cells, disposition directions of the shapes of the cells including the protrusions in the specific cells are different in one specific cell and other specific cells other than the one specific cell.

A honeycomb filter including: a pillar-shaped honeycomb structure including porous partition walls; and porous plugging portions disposed on either one of end portions of each of the cells, wherein a porosity (%) of the partition walls is defined as P1, a porosity (%) of the plugging portions is defined as P2, an occupancy (%) of the partition walls relative to an area of a cross section orthogonal to an extending direction of the cells of the honeycomb structure is defined as N1, the P1 is 50 to 65%, the P2 is 60 to 70%, the N1 is 22 to 39%, and X represented by Formula (1) satisfies a relation of Formula (2):
X=P1/P2N1,Formula (1):
18.800.19X.sup.2+11.33X121.6350.50.Formula (2):

A honeycomb filter includes a pillar-shaped honeycomb substrate and a plugging portion provided at an end portion on either an inflow or outflow end face side of cells, wherein, in a section orthogonal to the cell extending direction, the shapes of an inflow cell having the plugging portion and an outflow cell having the plugging portion are hexagonal. In the plurality of cells, a plurality of inflow cells surround one outflow cell such that one side of the inflow cell and one side of the outflow cell adjacent to the inflow cell are parallel. The partition wall includes a first partition wall and a second partition wall, at least one of the first partition walls is configured such that a ratio of a thickness of the second partition wall to the first partition wall is 1.0 to 2.5, and a total open frontal area is 35% to 95%.

A honeycomb structure body has a skin part of a cylindrical shape and a honeycomb structural part formed with the skin part together in a monolithic body. The skin part and the honeycomb structural part have partition walls of a porous structure. The cells have first cells arranged adjacent to the skin part and second cells arranged adjacent to the first cells. The skin part, the first cells and the second cells form an outer peripheral section. A central section is arranged inside the outer peripheral section. The honeycomb structure body satisfies a relationship in which a thermal expansion coefficient of the outer peripheral section is greater than a thermal expansion coefficient of the central section.

Provided is a honeycomb filter, including: a pillar-shaped honeycomb substrate having an inflow end face and an outflow end face and including a porous partition wall surrounding a plurality of cells; and a plugging portion disposed at any one of ends of the cells at the inflow end face and at the outflow end face. In a cross section orthogonal to an extending direction of the cells, inflow cells have a pentagonal or a hexagonal shape, and outflow cells have a square shape. The cells are configured that the inflow cells surround one outflow cell and one side of an inflow cell and one side of an adjacent outflow cell are parallel to each other. The partition wall is configured that thickness of a first partition wall disposed between the inflow cells and the outflow cells is smaller than thickness of a second partition wall disposed between the inflow cells.