Great snub dodecicosidodecahedron

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Great snub dodecicosidodecahedron
Great snub dodecicosidodecahedron.png
Bowers style acronymGisdid
Coxeter diagrams5/3s5/2s3*a (CDel branch hh.pngCDel split2-fp.pngCDel node h.png)
Faces20+60 triangles, 24 pentagrams
Vertex figureIrregular hexagon, edge lengths 1, 1, 1, (5–1)/2, 1, (5–1)/2
Great snub dodecicosidodecahedron vertfig.png
Measures (edge length 1)
Dihedral angles5/2–3 #1:
 5/2–3 #2:
Central density10
Number of pieces660
Level of complexity42
Related polytopes
ArmySemi-uniform srid
DualGreat hexagonal hexecontahedron
ConjugateGreat snub dodecicosidodecahedron
Abstract properties
Euler characteristic-16
Topological properties
SymmetryH3+, order 60

The great snub dodecicosidodecahedron, or gisdid, is a uniform polyhedron. It consists of 60 snub triangles, 20 more triangles, and 24 pentagrams that fall in coplanar pairs of one prograde, one retrograde. Four triangles and two pentagrams meet at each vertex.

It is the only chiral uniform polyhedron with an achiral convex hull. As such, it cannot be made into a compound with its reflection. If the pentagrams are removed, however, the disnub icosahedron is formed.

This polyhedron's edges are a subset of those of the great dirhombicosidodecahedron, and it shares the same vertices.

Vertex coordinates[edit | edit source]

A great snub dodecicosidodecahedron of edge length 1 has vertex coordinates given by all even permutations of:

Related polyhedra[edit | edit source]

o5/3o5/2o3*a truncations
Name OBSA CD diagram Picture
Great complex icosidodecahedron (degenerate, sissid+gike) gacid x5/3o5/2o3*a (CDel branch 10r.pngCDel split2-fp.pngCDel node.png)
Great complex icosidodecahedron.png
Great dodecicosidodecahedron gaddid x5/3x5/2o3*a (CDel branch 10r.pngCDel split2-fp.pngCDel node 1.png)
Great dodecicosidodecahedron.png
(degenerate, double cover of gissid) o5/3x5/2o3*a (CDel branch.pngCDel split2-fp.pngCDel node 1.png)
Great stellated dodecahedron.png
(degenerate, ditdid+gidtid) o5/3x5/2x3*a (CDel branch 01r.pngCDel split2-fp.pngCDel node 1.png)
Small ditrigonal icosidodecahedron.png
Great complex icosidodecahedron (degenerate, sissid+gike) gacid o5/3o5/2x3*a (CDel branch 01r.pngCDel split2-fp.pngCDel node.png)
Great complex icosidodecahedron.png
(degenerate, double cover of sidhei) x5/3o5/2x3*a (CDel branch 11.pngCDel split2-fp.pngCDel node.png)
Small dodecahemicosahedron.png
(degenerate, giddy+12(10/2)) x5/3x5/2x3*a (CDel branch 11.pngCDel split2-fp.pngCDel node 1.png)
Great snub dodecicosidodecahedron gisdid s5/3s5/2s2*a (CDel branch hh.pngCDel split2-fp.pngCDel node h.png)
Great snub dodecicosidodecahedron.png

External links[edit | edit source]