# Small dodecicosahedron

Small dodecicosahedron
Rank3
TypeUniform
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${\displaystyle {\sqrt {\frac {17+3{\sqrt {5}}}{8}}}\approx 1.72149}$
Dihedral angles6–10 #1: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }}$
6–10 #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }}$
Central densityeven
Number of external pieces320
Level of complexity18
Related polytopes
ArmySemi-uniform Srid, edge lengths ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$ (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.