Dodecahedral tegum

The dodecahedral tegum or dote, also called the dodecahedral bipyramid, is a convex isochoric polychoron with 24 pentagonal pyramids as cells. As the name suggests, it can be constructed as a tegum based on the dodecahedron.

It is the only tegum based on a Platonic solid that can't be made CRF.

In the variant obtained as the dual of the uniform icosahedral prism, the height from the top to the bottom vertex is $$2+\sqrt5 ≈ 4.23607$$ times the edge length of the base dodecahedron.