# Retrosphenoverted trispentachoron

Retrosphenoverted trispentachoron
Rank4
TypeUniform
Notation
Bowers style acronymRawvtip
Coxeter diagramo3x3x3/2o3*b ()
Elements
Cells5 octahedra, 5 truncated tetrahedra, 5 octahemioctahedra
Faces10+20+20 triangles, 20 hexagons
Edges30+60
Vertices30
Vertex figureCrossed wedge, edge lengths 1 (base square and top edge) and 3 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {35}}{5}}\approx 1.18632}$
Hypervolume${\displaystyle {\frac {47{\sqrt {5}}}{96}}\approx 1.09474}$
Dichoral anglesOho–3-oct: ${\displaystyle \arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }}$
Oho–6–tut: ${\displaystyle \arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }}$
Oct–3–tut: ${\displaystyle \arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }}$
Oho–3–oho: ${\displaystyle \arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }}$
Related polytopes
ArmySrip
RegimentSrip
ConjugateNone
Convex corePentachoron
Abstract & topological properties
Flag count1080
Euler characteristic–5
OrientableYes
Properties
SymmetryA4, order 120
ConvexNo
NatureTame

The retrosphenoverted trispentachoron, or rawvtip, is a nonconvex uniform polychoron that consists of 5 regular octahedra, 5 truncated tetrahedra, and 5 octahemioctahedra. 1 octahedron, 2 truncated tetrahedra, and 2 octahemioctahedra join at each vertex.

## Vertex coordinates

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