# Small ditrigonal dodecicosidodecahedral prism

Small ditrigonal dodecicosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymSidditdiddip
Coxeter diagramx x5/3o3x5*b ()
Elements
Cells20 triangular prisms, 12 pentagrammic prisms, 12 decagonal prisms, 2 small ditrigonal dodecicosidodecahedra
Faces40 triangles, 60+60 squares, 24 pentagrams, 24 decagons
Edges60+120+120
Vertices120
Vertex figureCrossed isosceles trapezoidal pyramid, edge lengths 1, (5+5)/2, (5–1)/2, (5+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {19+3{\sqrt {5}}}{8}}}\approx 1.79263}$
Hypervolume${\displaystyle 7{\frac {15+{\sqrt {5}}}{6}}\approx 20.10875}$
Dichoral anglesTrip–4–stiddip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
Sidditdid–5/2–stip: 90°
Sidditdid–3–trip: 90°
Sidditdid–10–dip: 90°
Stip–4–dip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Height1
Central density4
Number of external pieces238
Related polytopes
ArmySemi-uniform Sriddip
RegimentSiidip
DualSmall ditrigonal dodecacronic hexecontahedral tegum
ConjugateGreat ditrigonal dodecicosidodecahedral prism
Abstract & topological properties
Euler characteristic–18
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The small ditrigonal dodecicosidodecahedral prism or sidditdiddip is a prismatic uniform polychoron that consists of 2 small ditrigonal dodecicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 12 decagonal prisms. Each vertex joins 1 small ditrigonal dodecicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 decagonal prisms. As the name suggests, it is a prism based on the small ditrigonal dodecicosidodecahedron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedral prism.