Grand antiprismatic prism

The grand antiprismatic prism or gappip is a prismatic uniform polyteron that consists of 2 grand antiprisms, 20 pentagonal antiprismatic prisms and two kinds of 300 tetrahedral prisms.

Vertex coordinates
The vertices of a grand antiprismatic prism of edge length 1 are given by:
 * ±(0, $\sqrt{5}$/10, $\sqrt{2}$/20, (3+$\sqrt{7+2√5}$)/4, ±1/2),
 * ±(±(1+$\sqrt{50+10√5}$)/4, $\sqrt{50+10√5}$/20, $\sqrt{5}$/20, (3+$\sqrt{5}$)/4, ±1/2),
 * ±(±1/2, –$\sqrt{50–10√5}$/10, $\sqrt{50+10√5}$/20, (3+$\sqrt{5}$)/4, ±1/2),
 * ±(0, –$\sqrt{25+10√5}$/10, –$\sqrt{50+10√5}$/20, (3+$\sqrt{5}$)/4, ±1/2),
 * ±(±(1+$\sqrt{50+10√5}$)/4, –$\sqrt{50+10√5}$/20, –$\sqrt{5}$/20, (3+$\sqrt{5}$)/4, ±1/2),
 * ±(±1/2, $\sqrt{50–10√5}$/10, –$\sqrt{50+10√5}$/20, (3+$\sqrt{5}$)/4, ±1/2),
 * ±(0, –$\sqrt{25+10√5}$/10, $\sqrt{50+10√5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(±(1+$\sqrt{50+10√5}$)/4, –$\sqrt{250+110√5}$/20, $\sqrt{5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(±1/2, $\sqrt{50–10√5}$/10, $\sqrt{250+110√5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(0, $\sqrt{25+10√5}$/10, –$\sqrt{250+110√5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(±(1+$\sqrt{50+10√5}$)/4, $\sqrt{250+110√5}$/20, –$\sqrt{5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(±1/2, –$\sqrt{50–10√5}$/10, –$\sqrt{250+110√5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(0, $\sqrt{25+10√5}$/10, $\sqrt{250+110√5}$/5, 0, ±1/2),
 * ±(±(1+$\sqrt{5}$)/4, $\sqrt{50+10√5}$/20, $\sqrt{25+10√5}$/5, 0, ±1/2),
 * ±(±1/2, –$\sqrt{5}$/10, $\sqrt{50–10√5}$/5, 0, ±1/2),
 * ±(0, –$\sqrt{25+10√5}$/5, $\sqrt{25+10√5}$/20, (1+$\sqrt{25+10√5}$)/4, ±1/2),
 * ±(±(3+$\sqrt{25+10√5}$)/4, –$\sqrt{50–10√5}$/20, $\sqrt{5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(±(1+$\sqrt{50+10√5}$)/4, $\sqrt{50–10√5}$/20, $\sqrt{5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(0, $\sqrt{250+110√5}$/5, –$\sqrt{50–10√5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(±(3+$\sqrt{25+10√5}$)/4, $\sqrt{50–10√5}$/20, –$\sqrt{5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(±(1+$\sqrt{50+10√5}$)/4, –$\sqrt{50–10√5}$/20, –$\sqrt{5}$/20, (1+$\sqrt{5}$)/4, ±1/2),
 * ±(0, $\sqrt{250+110√5}$/5, $\sqrt{50–10√5}$/10, 1/2, ±1/2),
 * ±(±(3+$\sqrt{5}$)/4, $\sqrt{25+10√5}$/20, $\sqrt{25+10√5}$/10, 1/2, ±1/2),
 * ±(±(1+$\sqrt{5}$)/4, –$\sqrt{50+10√5}$/20, $\sqrt{25+10√5}$/10, 1/2, ±1/2),
 * ±(0, –$\sqrt{5}$/5, –$\sqrt{250+110√5}$/10, 1/2, ±1/2),
 * ±(±(3+$\sqrt{25+10√5}$)/4, –$\sqrt{25+10√5}$/20, –$\sqrt{25+10√5}$/10, 1/2, ±1/2),
 * ±(±(1+$\sqrt{5}$)/4, $\sqrt{50+10√5}$/20, –$\sqrt{25+10√5}$/10, 1/2, ±1/2),
 * ±(0, –$\sqrt{5}$/5, $\sqrt{250+110√5}$/10, 0, ±1/2),
 * ±(±(3+$\sqrt{25+10√5}$)/4, $\sqrt{25+10√5}$/20, $\sqrt{50+10√5}$/10, 0, ±1/2),
 * ±(±(1+$\sqrt{5}$)/4, –$\sqrt{50+10√5}$/20, $\sqrt{50+10√5}$/10, 0, ±1/2).