# Small dodecicosahedron

Small dodecicosahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSiddy
Elements
Faces20 hexagons, 12 decagons
Edges60+60
Vertices60
Vertex figureButterfly, edge lengths 3 and (5+5)/2
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{17+3\sqrt5}{8}} ≈ 1.72149}$
Dihedral angles6–10 #1: ${\displaystyle \arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768^\circ}$
6–10 #2: ${\displaystyle \arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ}$
Central densityeven
Number of external pieces320
Level of complexity18
Related polytopes
ArmySemi-uniform Srid, edge lengths ${\displaystyle \frac{\sqrt5-1}{2}}$ (pentagons), 1 (triangles)
RegimentSiid
DualSmall dodecicosacron
ConjugateGreat dodecicosahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–28
OrientableNo
Genus30
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The small dodecicosahedron, or siddy, is a uniform polyhedron. It consists of 20 hexagons and 12 decagons. Two hexagons and two decagons meet at each vertex..

It is a faceting of the small icosicosidodecahedron, using its 20 hexagons along with the 12 decagons of the small ditrigonal dodecicosidodecahedron.

## Vertex coordinates

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