Small dodecahemidodecahedron

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${\displaystyle {\frac {1+{\sqrt {5}}}{2}}\approx 1.61803}$
Dihedral angle${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
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

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

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