Small ditrigonary icosidodecahedral prism

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Small ditrigonary icosidodecahedral prism
Sidtiddip card Bowers.jpeg
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSidtiddip
Coxeter diagramx x5/2o3o3*b (CDel node 1.pngCDel 2.pngCDel branch.pngCDel split2-p3.pngCDel node 1.png)
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)
Circumradius1
Hypervolume
Dichoral anglesTrip–4–stip:
 Sidtid–3–trip: 90°
 Sidtid–5/2–stip: 90°
Height1
Central density2
Number of pieces74
Related polytopes
ArmySemi-uniform Dope
RegimentSidtiddip
DualSmall triambic icosahedral tegum
ConjugateGreat ditrigonary icosidodecahedral prism
Abstract properties
Euler characteristic–10
Topological properties
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[edit | edit source]

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:

along with all even permutations and all sign changes of:

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

External links[edit | edit source]