Small dodecicosidodecahedron

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Small dodecicosidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymSaddid
Coxeter diagramx3/2o5x5*a ()
Elements
Faces20 triangles, 12 pentagons, 12 decagons
Edges60+60
Vertices60
Vertex figureCrossed isosceles trapezoid, edge lengths 1, (5+5)/2, (1+5)/2, (5+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles5–10:
 3–10:
Central density2
Number of external pieces152
Level of complexity9
Related polytopes
ArmySrid
RegimentSrid
DualSmall dodecacronic hexecontahedron
ConjugateGreat dodecicosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–16
OrientableYes
Properties
SymmetryH3, order 120
Flag orbits4
ConvexNo
NatureTame

The small dodecicosidodecahedron, or saddid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 12 decagons. One triangle, one pentagon, and two decagons join at each vertex.

It is a faceting of the small rhombicosidodecahedron, using its 12 pentagons and 20 triangles along with 12 additional decagons.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

A small dodecicosidodecahedron has the following Coxeter diagrams:

  • x3/2o5x5*a ()
  • x5o3ß (, as holosnub)

External links[edit | edit source]