Step prism

A step prism is an isogonal polychoron whose vertices swirl in correspondence to a star polygon. The n-d step prism is a subsymmetrical faceting of an n-n duoprism.

The duals of the step prisms are called the gyrochora.

Construction
To construct the n-d step prism, one starts with a grid of n × n squares. One takes any vertex as the starting vertex, and repeatedly moves one step to the right, and d steps up. One identifies opposite edges of the square sheet: in other words, when one reaches the rightmost or the uppermost edge, one wraps around to the leftmost or to the lowermost edge, respectively. When one reaches the starting vertex, the grid is folded into an n-n duoprism. Finally, one takes the convex hull of all the traversed vertices.

An equivalent construction for the n-d step prism is as the convex hull of the vertices: for k ranging from 0 to n–1.
 * (cos(2πk/n), sin(2πk/n), cos(2πdk/n), sin(2πdk/n)),

Examples
5-2: Pentachoron

6-2: 3-3 duopyramid

7-2 and 7-3: 7-2 step prism

8-2: 8-2 step prism

8-3: Hexadecachoron

9-2 and 9-4: 9-2 step prism

9-3: 9-3 step prism

10-2: 10-2 step prism

10-3: Tetradisphenoidal triacontachoron

10-4: 5-5 duopyramid