Pentagonal-snub dodecahedral duoprism

The pentagonal-snub dodecahedral duoprism or pesnid is a convex uniform duoprism that consists of 5 snub dodecahedral prisms, 12 pentagonal duoprisms and 80 triangular-pentagonal duoprisms of two kinds. Each vertex joins 2 snub dodecahedral prisms, 4 triangular-pentagonal duoprisms, and 1 pentagonal duoprism.

Vertex coordinates
The vertices of a pentagonal-snub dodecahedral duoprism of edge length 1 are given by all even permutations with an odd number of sign changes of the last three coordinates of: as well as all even permutations with an even number of sign changes of the last three coordinates of: where
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,\frac{\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\xi\phi\sqrt{3-\xi^2}}2,\,\frac{\phi\sqrt{\xi(\xi+\phi)+1}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\, \sqrt{\frac{5-\sqrt5}{40}},\,\frac{\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\xi\phi\sqrt{3-\xi^2}}2,\,\frac{\phi\sqrt{\xi(\xi+\phi)+1}}2\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\xi\phi\sqrt{3-\xi^2}}2,\,\frac{\phi\sqrt{\xi(\xi+\phi)+1}}2\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,\frac{\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\phi\sqrt{\xi(\xi+1)}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\, \sqrt{\frac{5-\sqrt5}{40}},\,\frac{\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\phi\sqrt{\xi(\xi+1)}}2\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\phi\sqrt{\xi(\xi+1)}}2\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,\frac{\xi^2\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi\sqrt{\xi+1-\phi}}2,\,\frac{\sqrt{\xi^2(1+2\phi)-\phi}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\, \sqrt{\frac{5-\sqrt5}{40}},\,\frac{\xi^2\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi\sqrt{\xi+1-\phi}}2,\,\frac{\sqrt{\xi^2(1+2\phi)-\phi}}2\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{\xi^2\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi\sqrt{\xi+1-\phi}}2,\,\frac{\sqrt{\xi^2(1+2\phi)-\phi}}2\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,\frac{\xi^2\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi^2\sqrt{\xi(\xi+\phi)+1}}{2\xi}\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\, \sqrt{\frac{5-\sqrt5}{40}},\,\frac{\xi^2\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi^2\sqrt{\xi(\xi+\phi)+1}}{2\xi}\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{\xi^2\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi^2\sqrt{\xi(\xi+\phi)+1}}{2\xi}\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,\frac{\sqrt{\phi(\xi+2)+2}}2,\,\frac{\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\xi\sqrt{\xi(1+\phi)-\phi}}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\, \sqrt{\frac{5-\sqrt5}{40}},\,\frac{\sqrt{\phi(\xi+2)+2}}2,\,\frac{\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\xi\sqrt{\xi(1+\phi)-\phi}}2\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,\frac{\sqrt{\phi(\xi+2)+2}}2,\,\frac{\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\xi\sqrt{\xi(1+\phi)-\phi}}2\right),$$
 * $$\phi = \frac{1+\sqrt5}2,$$
 * $$\xi = \sqrt[3]{\frac{\phi+\sqrt{\phi-\frac5{27}}}2}+\sqrt[3]{\frac{\phi-\sqrt{\phi-\frac5{27}}}2}.$$