Small snub icosicosidodecahedral prism

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Small snub icosicosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSesidip
Coxeter diagramx2s5/2s3s3*b ()
Elements
Cells60 triangular prisms, 40 triangular prisms as 20 hexagrammic prisms, 12 pentagrammic prisms, 2 small snub icosicosidodecahedra
Faces120 triangles, 80 triangles as 40 hexagrams, 60+60+60 squares, 24 pentagrams
Edges60+120+120+120
Vertices120
Vertex figureMirror-symmetric hexagonal pyramid, edge lengths 1, 1, 1, 1, 1, (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dihedral anglesStip–4–trip:
 Trip–4–trip:
 Seside–5/2–stip: 90°
 Seside–3–trip: 90°
Height1
Central density2
Number of external pieces214
Related polytopes
ArmySemi-uniform Tipe
RegimentSesidip
DualSmall hexagonal hexecontahedral tegum
ConjugateSmall inverted retrosnub icosicosidodecahedral prism
Abstract & topological properties
Euler characteristic–30
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small snub icosicosidodecahedral prism or sesidip is a prismatic uniform polychoron that consists of 2 small snub icosicosidodecahedra, 12 pentagrammic prisms, and 40+60 triangular prisms (40 of which form compounds in the same hyperplane, with bases combining into hexagrams). Each vertex joins 1 small snub icosicosidodecahedron, 1 pentagrammic prism, and 5 triangular prisms. As the name suggests, it is a prism based on the small snub icosicosidodecahedron.

Vertex coordinates[edit | edit source]

A small snub icosicosidodecahedral prism of edge length 1 has vertex coordinates given by all even permutations of:

External links[edit | edit source]