Small icosihemidodecahedral prism

Small icosihemidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSeihiddip
Coxeter diagram(x x3/2o3x5*b)/2 ()
Elements
Cells20 triangular prisms, 6 decagonal prisms, 2 small icosihemidodecahedra
Faces40 triangles, 60 squares, 12 decagons
Edges30+120
Vertices60
Vertex figureBowtie pyramid, edge lengths 1, (5+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7+2{\sqrt {5}}}}{2}}\approx 1.69353}$
Dichoral anglesSeihid–3–trip: 90°
Seihid–10–dip: 90°
Trip–4–dip: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
Height1
Number of external pieces120
Related polytopes
ArmyIddip
RegimentIddip
DualSmall icosihemidodecacronic tegum
ConjugateGreat icosihemidodecahedral prism
Abstract & topological properties
Euler characteristic–6
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small icosihemidodecahedral prism or seihiddip, is a prismatic uniform polychoron that consists of 2 small icosihemidodecahedra, 20 triangular prisms, and 6 decagonal prisms. Each vertex joins 1 small icosihemidodecahedron, 2 triangular prisms, and 2 decagonal prisms. As the name suggests, it is a prism based on the small icosihemidodecahedron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the icosidodecahedral prism.