Pentagonal trioprism

The pentagonal trioprism or pettip is a convex uniform trioprism that consists of 15 pentagonal duoprismatic prisms.

Vertex coordinates
The vertices of a pentagonal trioprism of edge length 1 are given by:
 * (0, $\sqrt{150+30√5}$/10, 0, $\sqrt{50+10√5}$/10, 0, $\sqrt{50+10√5}$/10),
 * (0, $\sqrt{50+10√5}$/10, 0, $\sqrt{50+10√5}$/10, ±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20),
 * (0, $\sqrt{50–10√5}$/10, 0, $\sqrt{50+10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10),
 * (0, $\sqrt{25+10√5}$/10, ±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/10),
 * (0, $\sqrt{50+10√5}$/10, ±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20),
 * (0, $\sqrt{50–10√5}$/10, ±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20, ±1/2, –$\sqrt{50–10√5}$/10),
 * (0, $\sqrt{25+10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10, 0, $\sqrt{25+10√5}$/10),
 * (0, $\sqrt{50+10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10, ±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$/20),
 * (0, $\sqrt{50–10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10),
 * (±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/10, 0, $\sqrt{50+10√5}$/10),
 * (±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/10, ±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20),
 * (±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10),
 * (±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/10),
 * (±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20),
 * (±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20, ±1/2, –$\sqrt{50–10√5}$/10),
 * (±1/2, –$\sqrt{25+10√5}$/10, 0, $\sqrt{25+10√5}$/10, 0, $\sqrt{50+10√5}$/10),
 * (±1/2, –$\sqrt{50+10√5}$/10, 0, $\sqrt{25+10√5}$/10, ±(1+$\sqrt{50+10√5}$)/4, $\sqrt{5}$/20),
 * (±1/2, –$\sqrt{50–10√5}$/10, 0, $\sqrt{25+10√5}$/10, ±1/2, –$\sqrt{50+10√5}$/10),
 * (±1/2, –$\sqrt{25+10√5}$/10, ±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$/20, 0, $\sqrt{50–10√5}$/10),
 * (±1/2, –$\sqrt{50+10√5}$/10, ±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$/20, ±(1+$\sqrt{50–10√5}$)/4, $\sqrt{5}$/20),
 * (±1/2, –$\sqrt{50–10√5}$/10, ±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$/20, ±1/2, –$\sqrt{50–10√5}$/10),
 * (±1/2, –$\sqrt{25+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10, 0, $\sqrt{25+10√5}$/10),
 * (±1/2, –$\sqrt{50+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10, ±(1+$\sqrt{25+10√5}$)/4, $\sqrt{5}$/20),
 * (±1/2, –$\sqrt{50–10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10, ±1/2, –$\sqrt{25+10√5}$/10).