# Grand rhombic prismatopentachoron

(Redirected from Garpop)
Grand rhombic prismatopentachoron
Rank4
TypeUniform
Notation
Bowers style acronymGarpop
Coxeter diagramx3x3/2x3/2x ()
Elements
Cells10 hexagonal prisms, 5 cubohemioctahedra
Faces15+30 squares, 20 hexagons
Edges30+60
Vertices30
Vertex figureCrossed butterfly wedge, edge lengths 2 (6) and 3 (4)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {35}}{5}}\approx 1.18632}$
Dichoral anglesCho–4–hip: ${\displaystyle \arccos \left({\frac {\sqrt {6}}{6}}\right)\approx 65.90516^{\circ }}$
Cho–6–hip: ${\displaystyle \arccos \left({\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }}$
Hip–4–hip: ${\displaystyle \arccos \left({\frac {2}{3}}\right)\approx 48.18968^{\circ }}$
Related polytopes
ArmySrip
RegimentSrip
ConjugateNone
Convex coreJoined pentachoron
Abstract & topological properties
Flag count1200
Euler characteristic–10
OrientableNo
Properties
SymmetryA4, order 120
ConvexNo
NatureTame

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.