Grand rhombic prismatopentachoron

Grand rhombic prismatopentachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Garpop
Coxeter diagram	x3x3/2x3/2x ()
Elements
Cells	10 hexagonal prisms, 5 cubohemioctahedra
Faces	15+30 squares, 20 hexagons
Edges	30+60
Vertices	30
Vertex figure	Crossed butterfly wedge, edge lengths √2 (6) and √3 (4)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {35}}{5}}\approx 1.18632$
Dichoral angles	Cho–4–hip: $\arccos \left({\frac {\sqrt {6}}{6}}\right)\approx 65.90516^{\circ }$
	Cho–6–hip: $\arccos \left({\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }$
	Hip–4–hip: $\arccos \left({\frac {2}{3}}\right)\approx 48.18968^{\circ }$
Related polytopes
Army	Srip
Regiment	Srip
Conjugate	None
Convex core	Joined pentachoron
Abstract & topological properties
Flag count	1200
Euler characteristic	–10
Orientable	No
Properties
Symmetry	A4, order 120
Convex	No
Nature	Tame

The grand rhombic prismatopentachoron, or garpop, is a nonconvex uniform polychoron that consists of 5 cubohemioctahedra and 10 hexagonal prisms. 2 cubohemioctahedra and 10 hexagonal prisms join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated pentachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#137).

• Klitzing, Richard. "garpop".