Step prism

A step prism is an isogonal polychoron whose vertices swirl corresponding to a star polygon (Schläfli symbol {n/d}). In other words, they are subsymmetrical vertex-facetings of an n-n duoprism.

Its dual is called a gyrochoron.

Construction
To construct a step prism, take a grid of n x n squares (it is important to note that if you go to the last vertex, the next vertex will wrap to the opposite side, which is topologically represented as a duocylinder). From a given starting vertex, move right a number of steps to reach the next vertex until you reach the starting vertex again, then fold the grid into an n-n duoprism. Then take the convex hull of the selected vertices. The resulting polychoron will be an n-d step prism, where n is the number of vertices in a column or row and d is the number of steps from a previous vertex).

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