Decachoric prism

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Decachoric prism
File:Decachoric prism.png
Rank5
TypeUniform
Notation
Bowers style acronymDecap
Coxeter diagramx o3x3x3o ()
Elements
Tera10 truncated tetrahedral prisms, 2 decachora
Cells20 triangular prisms, 20 hexagonal prisms, 20 truncated tetrahedra
Faces40 triangles, 60 squares, 40 hexagons
Edges30+120
Vertices60
Vertex figureTetragonal disphenoidal pyramid, edge lengths 1, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTuttip–hip–tuttip:
 Deca–tut–tuttip: 90°
 Tuttip–trip–tuttip:
Height1
Central density1
Number of external pieces12
Level of complexity15
Related polytopes
ArmyDecap
RegimentDecap
DualBidecachoric tegum
ConjugateNone
Abstract & topological properties
Flag count7200
Euler characteristic2
OrientableYes
Properties
SymmetryA4×2×A1, order 480
ConvexYes
NatureTame

The decachoric prism or decap is a prismatic uniform polyteron that consists of 2 decachora and 10 truncated tetrahedral prisms. 1 decachoron and 4 truncated tetrahedral prisms join at each vertex. As the name suggests, it can be obtained as a prism based on the decachoron, which also makes it a convex segmentoteron.

Vertex coordinates[edit | edit source]

The vertices of a decachoric prism of edge length 1 are given by:

External links[edit | edit source]