S5S5

S5S5 or double-ess-five is a non-convex regular faced polyhedron. It can be formed as an outer-blend of two pentagonal antiprisms.

Vertex coordinates
Vertex coordinates for S5S5 with unit side length can be given as
 * $$\left(\pm\frac{1}{2},\,-\sqrt{\frac{5+2\sqrt{5}}{20}},\,0\right)$$,
 * $$\left(\pm\frac{1}{2},\,\sqrt{\frac{5+2\sqrt{5}}{20}},\,\pm\sqrt{\frac{5+\sqrt{5}}{10}}\right)$$,
 * $$\left(\pm\frac{1+\sqrt{5}}{4},\,\sqrt{\frac{5-\sqrt{5}}{40}},\,0\right)$$,
 * $$\left(\pm\frac{1+\sqrt{5}}{4},\,-\sqrt{\frac{5-\sqrt{5}}{40}},\,\pm\sqrt{\frac{5+\sqrt{5}}{10}}\right)$$,
 * $$\left(0,\,\sqrt{\frac{5+\sqrt{5}}{10}},\,0\right)$$,
 * $$\left(0,\,-\sqrt{\frac{5+\sqrt{5}}{10}},\,\pm\sqrt{\frac{5+\sqrt{5}}{10}}\right)$$.

Related polyhedra


The relative positioning of its pentagonal faces makes S5S5 useful for tunnelling Stewart toroids. In many cases S5S5 can be substituted for another polyhedron with the same configuration of pentagonal faces.