Skew compound of six pentagons

The  is a regular skew compound polygon made of six planar pentagons.

Vertex coordinates


The has the same vertices as a icosidodecahedron. With unit side length vertex coordinates are given by all permutations of and even permutations of
 * $$\left(\pm\sqrt{\frac{5+\sqrt{5}}{10}},\,0,\,0\right)$$
 * $$\left(\pm\sqrt{\frac{5+\sqrt{5}}{20}},\,\pm\sqrt{\frac{5 +\sqrt{5}}{40}},\,\pm\sqrt{\frac{5 -\sqrt{5}}{40}}\right)$$

Stellation
The can also be stellated to form another regular skew compound polygon; the skew compound of six pentagrams. Because it is a compound this is simply the same as stellating each pentagon separately.