# Small snub icosicosidodecahedral prism

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${\displaystyle {\frac {\sqrt {17+3{\sqrt {5}}+{\sqrt {102+46{\sqrt {5}}}}}}{4}}\approx 1.54153}$
Hypervolume${\displaystyle {\frac {45+39{\sqrt {5}}+5{\sqrt {302+150{\sqrt {5}}}}}{12}}\approx 21.53680}$
Dihedral anglesStip–4–trip: ${\displaystyle \arccos \left(-{\sqrt {\frac {15-2{\sqrt {5}}+2{\sqrt {30{\sqrt {5}}-65}}}{15}}}\right)\approx 161.02258^{\circ }}$
Trip–4–trip: ${\displaystyle \arccos \left(-{\frac {\sqrt {3+2{\sqrt {5}}}}{3}}\right)\approx 155.66804^{\circ }}$
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

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

• ${\displaystyle \left(0,\,\pm {\frac {3+{\sqrt {3+2{\sqrt {5}}}}}{4}},\,\pm {\frac {1-{\sqrt {5}}+{\sqrt {6{\sqrt {5}}-2}}}{8}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}+{\sqrt {3+2{\sqrt {5}}}}}{4}},\,\pm {\frac {{\sqrt {5}}-1+{\sqrt {6{\sqrt {5}}-2}}}{8}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1+{\sqrt {3+2{\sqrt {5}}}}}{4}},\,\pm {\frac {3+{\sqrt {5}}+{\sqrt {6{\sqrt {5}}-2}}}{8}},\,\pm {\frac {1}{2}}\right).}$