Great dodecicosidodecahedral prism

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Great dodecicosidodecahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGaddiddip
Coxeter diagramx x5/3x5/2o3*b (CDel node 1.pngCDel 2.pngCDel label5-2.pngCDel branch 10ru.pngCDel split2-f3.pngCDel node 1.png)
Elements
Cells20 triangular prisms, 12 pentagrammic prisms, 12 decagrammic prisms, 2 great dodecicosidodecahedra
Faces40 triangles, 60+60 squares, 24 pentagrams, 24 decagrams
Edges60+120+120
Vertices120
Vertex figureIsosceles trapezoidal pyramid, edge lengths 1, (5–5)/2, (5–1)/2, (5–5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesStip–4–stiddip:
 Trip–4–stiddip:
 Gaddid–5/2–stip: 90°
 Gaddid–3–trip: 90°
 Gaddid–10/3–stiddip: 90°
Height1
Central density10
Number of pieces182
Related polytopes
ArmySemi-uniform Tipe
RegimentGaddiddip
DualGreat dodecacronic hexecontahedral tegum
ConjugateSmall dodecicosidodecahedral prism
Abstract properties
Euler characteristic–18
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

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

The great dodecicosidodecahedral prism can be vertex-inscribed into the grand ditetrahedronary hexacosidishecatonicosachoron.

Vertex coordinates[edit | edit source]

The vertices of a great dodecicosidodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

along with all even permutations of the first three coordinates of:

External links[edit | edit source]