# Small icosihemidodecahedron

Small icosihemidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymSeihid
Coxeter diagram(x3/2o3x5*a)/2
()/2
Elements
Faces20 triangles, 6 decagons
Edges60
Vertices30
Vertex figureBowtie, edge lengths 1 and (5+5)/2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1+{\sqrt {5}}}{2}}\approx 1.61803}$
Dihedral angle${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
Number of external pieces80
Level of complexity4
Related polytopes
ArmyId
RegimentId
DualSmall icosihemidodecacron
ConjugateGreat icosihemidodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–4
OrientableNo
Genus6
Properties
SymmetryH3, order 120
Flag orbits2
ConvexNo
NatureTame

The small icosihemidodecahedron, or seihid, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 20 equilateral triangles and 6 central decagons, with two of each joining at a vertex.

It can be derived as a rectified petrial dodecahedron.

It is a faceting of the icosidodecahedron, keeping the original's triangles while also using its equatorial decagons.

## Name

Its triangular faces are parallel to those of an icosahedron, and its hemi decagonal faces are parallel to those of a dodecahedron, hence the name "icosihemidodecahedron". The "small" prefix, used for stellations in general, distinguishes it from the great icosihemidodecahedron, which also has this face arrangement.

## Vertex coordinates

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