(10,2)-polysphericon

The (10,2)-polysphericon is a prime polysphericon. It is the smallest prime polysphericon not equivalent to a ($r$,1)-polysphericon.

It can be constructed by taking the solid of rotation of a decagon, bisecting it along a decagon, rotating one half by $$\frac{2\pi}{5}$$, and recombining the two halves along their decagonal faces. It corresponds to the polygon.