# Rhombiprismic dispentachoron

The rhombiprismic dispentachoron, or ripdip, is a nonconvex uniform polychoron that consists of 5 cubohemioctahedra, 5 truncated octahedra, and 10 hexagonal prisms. One cubohemioctahedron, two truncated octahedra, and two hexagonal prisms join at each vertex.

Rhombiprismic dispentachoron
Rank4
TypeUniform
Notation
Bowers style acronymRipdip
Elements
Cells10 hexagonal prisms, 5 cubohemioctahedra, 5 truncated octahedra
Faces30+30 squares, 20+20 hexagons
Edges30+60+60
Vertices60
Vertex figureSkewed bowtie pyramid, base edge lengths 2, 3, 2, 3; lateral edge lengths 2, 2, 3, 3
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {65}}{5}}\approx 1.61245}$
Dichoral anglesCho–4–hip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{6}}\right)\approx 114.09484^{\circ }}$
Cho–6–toe: ${\displaystyle \arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }}$
Toe–4–hip: ${\displaystyle \arccos \left({\frac {\sqrt {6}}{6}}\right)\approx 65.95106^{\circ }}$
Toe-6-hip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }}$
Related polytopes
ArmyPrip
RegimentPrip
ConjugateNone
Abstract & topological properties
Flag count1920
Euler characteristic–10
OrientableNo
Properties
SymmetryA4, order 120
ConvexNo
NatureTame

## Vertex coordinates

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