Skew icosahedron

The  is a regular skew polyhedron in 6-dimensional Euclidean space. It is abstractly equivalent to the regular icosahedron in 3-dimensional Euclidean space. It can be constructed as the blend of the icosahedron and the great icosahedron $$\{3,5 \} \# \{ 3, 5/2 \}$$.

Vertex coordinates
Vertex coordinates for a with unit edge length centered at the origin can be given as:


 * $$\pm\dfrac{\sqrt{2}}{4}\left(1,\,1,\,1,\,1,\,1,\,1\right)$$,
 * $$\pm\dfrac{\sqrt{2}}{4}\left(-1,\,-1,\,1,\,1,\,1,\,1\right)$$,
 * $$\pm\dfrac{\sqrt{2}}{4}\left(1,\,-1,\,-1,\,1,\,1,\,1\right)$$,
 * $$\pm\dfrac{\sqrt{2}}{4}\left(1,\,1,\,-1,\,-1,\,1,\,1\right)$$,
 * $$\pm\dfrac{\sqrt{2}}{4}\left(1,\,1,\,1,\,-1,\,-1,\,1\right)$$,
 * $$\pm\dfrac{\sqrt{2}}{4}\left(-1,\,1,\,1,\,1,\,-1,\,1\right)$$.

Related polyhedra
Just as the 3-dimensional icosahedron can be facetted to form the great dodecahedron, the can be facetted to form a regular skew great dodecahedron.