Small dodecahemidodecahedron

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Small dodecahemidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymSidhid
Coxeter diagram(x5/4o5x5*a)/2
()/2
Elements
Faces
Edges60
Vertices30
Vertex figureBowtie, edge lengths (1+5)/2 and (5+5)/2
Measures (edge length 1)
Circumradius
Dihedral angle
Number of external pieces72
Level of complexity4
Related polytopes
ArmyId
RegimentId
DualSmall dodecahemidodecacron
ConjugateGreat dodecahemidodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–12
OrientableNo
Genus14
Properties
SymmetryH3, order 120
Flag orbits2
ConvexNo
NatureTame

The small dodecahemidodecahedron, or sidhid, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 12 pentagons and 6 "hemi" decagons, with two of each joining at a vertex.

It can be derived as a rectified petrial icosahedron.

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

Naming[edit | edit source]

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

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]