Small icosicosidodecahedron

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Small icosicosidodecahedron
Small icosicosidodecahedron.png
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSiid
Coxeter diagramx5/2o3x3*a (CDel label5-2.pngCDel branch 10ru.pngCDel split2.pngCDel node 1.png)
Elements
Faces20 triangles, 12 pentagrams, 20 hexagons
Edges60+60
Vertices60
Vertex figureIsosceles trapezoid, edge lengths 1, 3, (5–1)/2, 3
Small icosicosidodecahedron vertfig.png
Measures (edge length 1)
Circumradius
Volume
Dihedral angles5/2–6:
 3–6:
Central density2
Number of pieces92
Level of complexity7
Related polytopes
ArmySemi-uniform Srid
RegimentSiid
DualSmall icosacronic hexecontahedron
ConjugateGreat icosicosidodecahedron
Convex coreTruncated icosahedron
Abstract properties
Euler characteristic–8
Topological properties
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The small icosicosidodecahedron, or siid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 20 hexagons. One triangle, one pentagram, and two hexagons join at each vertex.

A semi-uniform variant of this polyhedron can be constructed as a rectified small ditrigonary icosidodecahedron.

Vertex coordinates[edit | edit source]

A small icosicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:

Representations[edit | edit source]

A small icosicosidodecahedron has the following Coxeter diagrams:

  • x5/2o3x3*a
  • ß5o3x (as holosnub)

Related polyhedra[edit | edit source]

The small icosicosidodecahedron is the colonel of a three-member regiment that also includes the small ditrigonal dodecicosidodecahedron and the small dodecicosahedron.

o5/2o3o3*a truncations
Name OBSA CD diagram Picture
Small ditrigonary icosidodecahedron sidtid x5/2o3o3*a (CDel branch.pngCDel split2-p3.pngCDel node 1.png)
Small ditrigonal icosidodecahedron.png
(degenerate, double cover of id) x5/2x3o3*a (CDel branch 10r.pngCDel split2-p3.pngCDel node 1.png)
Icosidodecahedron.png
(degenerate, double cover of ike) o5/2o3x3*a (CDel branch 01r.pngCDel split2-p3.pngCDel node.png)
Icosahedron.png
Small icosicosidodecahedron siid x5/2o3x3*a (CDel branch 01r.pngCDel split2-p3.pngCDel node 1.png)
Small icosicosidodecahedron.png
(degenerate, double cover of ti) x5/2x3x3*a (CDel branch 11.pngCDel split2-p3.pngCDel node 1.png)
Truncated icosahedron.png
Small snub icosicosidodecahedron seside s5/2s3s3*a (CDel branch hh.pngCDel split2-p3.pngCDel node h.png)
Small snub icosicosidodecahedron.png

External links[edit | edit source]