Duoprism

The n-m duoprism is a polychoron formed as the prism product of a regular n-gon and a regular m-gon. n and m are here Schlafli symbols of any regular polygon, including not just integers but also fractions denoting star polygons like 5/2. The relative sizes of the two input polygons are unspecified, but if they both have the same edge length then the resulting figure is uniform.

Duoprisms are vertex-transitive, and also cell-transitive if m = n. The term "duoprism" originated in the hi.gher.space community. In the same way that regular polygons are discrete versions of circles, duoprisms discretize the Clifford torus (the Cartesian product of two circles).

Vertex coordinates

The n/d-m/e duoprism has vertices located at

$\left(\cos {\frac {2\pi i}{n}},\sin {\frac {2\pi i}{n}},x\cos {\frac {2\pi j}{m}},x\sin {\frac {2\pi j}{m}}\right)$

where $0\leq i<n$ and $0\leq j<m$ are both integers, and $x\neq 0$ is a real number. If d = e = 1, then the duoprism is convex, and the figure is precisely the convex hull of these vertices.

Related polytopes

The step prisms are facetings of duoprisms, retaining a subset of the vertices but changing all other elements.