# Small dodecahemicosahedron

Small dodecahemicosahedron
Rank3
TypeUniform
Notation
Bowers style acronymSidhei
Coxeter diagram()/2
(x5/3o5/2x3*a)/2
Elements
Faces
Edges60
Vertices30
Vertex figureBowtie, edge lengths (5–1)/2 and 3
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
Number of external pieces240
Level of complexity12
Related polytopes
ArmyId, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentDid
DualSmall dodecahemicosacron
ConjugateGreat dodecahemicosahedron
Abstract & topological properties
Flag count240
Euler characteristic–8
OrientableNo
Genus10
Properties
SymmetryH3, order 120
Flag orbits2
ConvexNo
NatureTame

The small dodecahemicosahedron, or sidhei, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagrams and 10 "hemi" hexagons, with two of each joining at a vertex.

It can be derived as a rectified Petrial great dodecahedron.

It is a faceting of the dodecadodecahedron, keeping the original's pentagrams while also using its equatorial hexagons.

## Name

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

## Vertex coordinates

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