Trigyrate rhombicosidodecahedron

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Trigyrate rhombicosidodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymTagyrid
Elements
Faces1+1+3+3+6+6 triangles, 3+3+3+3+6+6+6 squares, 3+3+3+3 pentagons
Edges8×3+16×6
Vertices3+3+3+3+6+6+6+6+6+6+6+6
Vertex figures15+15 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 30 irregular tetragons, edge lengths 1, 2, 2, (1+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3–4:
 3–5:
 4–4:
 4–5:
Central density1
Number of external pieces62
Level of complexity80
Related polytopes
ArmyTagyrid
RegimentTagyrid
DualTrideltogyrate deltoidal hexecontahedron
ConjugateTrigyrate quasirhombicosidodecahedron
Abstract & topological properties
Flag count480
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×I, order 6
ConvexYes
NatureTame

The trigyrate rhombicosidodecahedron is one of the 92 Johnson solids (J75). It consists of 1+1+3+3+6+6 triangles, 3+3+3+3+6+6+6 squares, and 3+3+3+3 pentagons. It can be constructed by rotating three mutually non-adjacent pentagonal cupolaic caps of the small rhombicosidodecahedron by 36°.

Vertex coordinates[edit | edit source]

A trigyrate rhombicosidodecahedron of edge length 1 has vertices given by:

External links[edit | edit source]