# Small dodecahemicosahedron

(Redirected from Sidhei)
Small dodecahemicosahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSidhei
Coxeter diagram()/2
(x5/3o5/2x3*a)/2
Elements
Faces12 pentagrams, 10 hexagons
Edges60
Vertices30
Vertex figureBowtie, edge lengths (5–1)/2 and 3
Measures (edge length 1)
Dihedral angle${\displaystyle \arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768^\circ}$
Number of pieces240
Level of complexity12
Related polytopes
ArmyId
RegimentDid
DualSmall dodecahemicosacron
ConjugateGreat dodecahemicosahedron
Abstract properties
Euler characteristic–8
Topological properties
OrientableNo
Genus10
Properties
SymmetryH3, order 120
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. Its pentagrammic faces are parallel to those of a dodecahedron, and its hemi hexagonal faces are parallel to those of an icosahedron: hence the name "dodecahemicosahedron". The "small" suffix, used for stellations in general, distinguishes it from the great dodecahemicosahedron, which also has this face arrangement.

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

## Vertex coordinates

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