Great stellated truncated dodecahedron explained

Related polyhedra

It shares its vertex arrangement with three other uniform polyhedra: the small icosicosidodecahedron, the small ditrigonal dodecicosidodecahedron, and the small dodecicosahedron:

Cartesian coordinates

Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of $\begin \Bigl(& 0,& \pm\,\varphi,& \pm \bigl[2-\frac{1}{\varphi}\bigr] &\Bigr) \\ \Bigl(& \pm\,\varphi,& \pm\,\frac,& \pm\,\frac &\Bigr) \\ \Bigl(& \pm\,\frac,& \pm\,\frac,& \pm\,2 &\Bigr) \end$

where

\varphi=\tfrac{1+\sqrt5}{2}

is the golden ratio.

Notes and References

Web site: 66: great stellated truncated dodecahedron. Maeder. Roman. MathConsult.

Great stellated truncated dodecahedron explained

Related polyhedra

Cartesian coordinates

See also

Notes and References