Dodecadodecahedral prism

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Dodecadodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymDiddip
Coxeter diagramx o5/2x5o ()
Elements
Cells12 pentagonal prisms, 12 pentagrammic prisms, 2 dodecadodecahedra
Faces60 squares, 24 pentagons, 24 pentagrams
Edges30+120
Vertices60
Vertex figureRectangular pyramid, edge lengths (1+5)/2, (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume5
Dichoral anglesPip–4–stip:
 Did–5–pip: 90°
 Did–5/2–stip: 90°
Height1
Central density3
Number of external pieces74
Related polytopes
ArmySemi-uniform Iddip
RegimentDiddip
DualMedial rhombic triacontahedral tegum
Conjugatedodecadodecahedral prism
Abstract & topological properties
Euler characteristic–8
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The dodecadodecahedral prism or diddip, is a prismatic uniform polychoron that consists of 2 dodecadodecahedra, 12 pentagrammic prisms, and 12 pentagonal prisms. Each vertex joins 1 dodecadodecahedron, 2 pentagrammic prisms, and 2 pentagonal prisms. As the name suggests, it is a prism based on the dodecadodecahedron.

Cross-sections[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.


Vertex coordinates[edit | edit source]

The vertices of a dodecadodecahedral 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]