# Small rhombic dispentachoron

Small rhombic dispentachoron
Rank4
TypeUniform
Notation
Bowers style acronymSirdop
Coxeter diagram
Elements
Cells10 triangular prisms, 5 truncated tetrahedra, 5 cubohemioctahedra
Faces20 triangles, 30 squares, 20 hexagons
Edges30+60
Vertices30
Vertex figureButterfly wedge, edge lengths 1 (bases), 2 (sides of outer triangles), and 3 (sides of inner triangles)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {35}}{5}}\approx 1.18322}$
Dichoral anglesCho–4–trip: ${\displaystyle \arccos \left(-{\frac {\sqrt {6}}{6}}\right)\approx 114.09484^{\circ }}$
Cho–6–tut: ${\displaystyle \arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }}$
Tut–3–trip: ${\displaystyle \arccos \left({\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }}$
Related polytopes
ArmySrip
RegimentSrip
ConjugateNone
Convex corePentachoron
Abstract & topological properties
Flag count1200
Euler characteristic–10
OrientableNo
Properties
SymmetryA4, order 120
ConvexNo
NatureTame

The small rhombic dispentachoron, or sirdop, is a nonconvex uniform polychoron that consists of 5 truncated tetrahedra, 5 cubohemioctahedra, and 10 triangular prisms. 2 of each type of cell join at each vertex.

## Vertex coordinates

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