Unfortunately, In[1142]:= PolyhedronData["Endododecahedron", "Volume"] // N During evaluation of In[1142]:= PolyhedronData::notdef: PolyhedronData has no value associated with the specified argument(s). The faces of the endododecahedron <http://gosper.org/endogram.png> are the equilateral trousers <http://gosper.org/starpants.png> (waistband = inseam = outseam) of a regular pentagram. —rwg The volume of the endodec inscribed in the unit cube (its convex hull) is tiny: 2 - PolyhedronData["Dodecahedron", "Volume"]/ GoldenRatio^3 // FullSimplify Out[1128]= 1/(3 + Sqrt[5]) = ϕ⁻²/2 ~ 0.190983005625053. in disagreement with (at least the first edition of) The Symmetries of Things. Has it been corrected? https://en.wikipedia.org/wiki/Dodecahedron#/media/File:Endo-dodecahedron_hon... https://www.reddit.com/r/mathpics/comments/572fpu/endododecahedron/