# Small ditrigonary icosidodecahedral prism

Small ditrigonary icosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSidtiddip
Coxeter diagramx x5/2o3o3*b ()
Elements
Cells20 triangular prisms, 12 pentagrammic prisms, 2 small ditrigonary icosidodecahedra
Faces40 triangles, 60 squares, 24 pentagrams
Edges20+120
Vertices40
Vertex figureditrigonal pyramid, edge lengths 1, (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Hypervolume${\displaystyle {\frac {4{\sqrt {5}}}{3}}\approx 2.98142}$
Dichoral anglesTrip–4–stip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 142.62263^{\circ }}$
Sidtid–3–trip: 90°
Sidtid–5/2–stip: 90°
Height1
Central density2
Number of external pieces74
Related polytopes
ArmySemi-uniform Dope
RegimentSidtiddip
DualSmall triambic icosahedral tegum
ConjugateGreat ditrigonary icosidodecahedral prism
Abstract & topological properties
Euler characteristic–10
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small ditrigonary icosidodecahedral prism or sidtiddip, is a prismatic uniform polychoron that consists of 2 small ditrigonary icosidodecahedra, 12 pentagrammic prisms, and 20 triangular prisms. Each vertex joins 1 small ditrigonary icosidodecahedron, 3 pentagrammic prisms, and 3 triangular prisms. As the name suggests, it is a prism based on the small ditrigonary icosidodecahedron.

The small ditrigonary icosidodecahedral prism can be vertex-inscribed into the small stellated hecatonicosachoron.

## Vertex coordinates

The vertices of a small ditrigonary icosidodecahedral prism of edge length 1 are given by all permutations and changes of sign of the first three coordinates of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),}$

along with all even permutations and all sign changes of:

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

The first set of vertices are those of an inscribed tesseract, seen as a cubic prism.