A staircase is provided that includes a column and steps. Each step: is coupled to the column and extends outside of, and away from, the column; includes a tread surface; and can move longitudinally along the column. The staircase can transition to a plurality of states by an actuation system, including closed and open states. The closed state includes the steps positioned at the upper end with the tread surfaces of the plurality of steps oriented around the upper end and coplanar to a flooring surface of the upper floor. The opened state includes the steps positioned at varying distances longitudinally along the column from the upper end towards the lower end so as to form spiraling steps around the column between the upper and lower floors. The steps can move longitudinally along the column for positioning in the closed and opened states.

An improved folding stair comprising a sequence of steps (101), each rotably mounted to a structure (102) via axes (103) located and oriented to facilitate rotation between deployed and stowed states, such that the steps exhibit tread overhang (109) in their deployed state. The step width (105) exceeds the step rise (107). In other embodiments the axes are to one side of the steps. In other embodiments the angle of rotation between deployed and stowed states exceeds the arccosine of step-above thickness (104) over step rise. In other embodiments the movement from deployed to stowed state moves the steps from the traversal path. In other embodiments the axes are either skew to the deployed tread, or to the traversal path, or to both. Other embodiments include a means of coordinating the steps' folding motion.