Truncated icositetrachoric prism

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Truncated icositetrachoric prism
File:Truncated icositetrachoric prism.png
Rank5
TypeUniform
Notation
Bowers style acronymTicope
Coxeter diagramx x3x4o3o
Elements
Tera24 tesseracts, 24 truncated octahedral prisms, 2 truncated icositetrachora
Cells48+144 cubes, 96 hexagonal prisms, 48 truncated octahedra
Faces96+288+288 squares, 192 hexagons
Edges192+192+576
Vertices384
Vertex figureTriangular pyramidal pyramid, edge lengths 2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume159
Diteral anglesTes–cube–tope: 135°
 Tope–hip–tope: 120°
 Tico–toe–tope: 90°
 Tico–cube–tes: 90°
Height1
Central density1
Number of external pieces50
Level of complexity20
Related polytopes
ArmyTicope
RegimentTicope
DualOctakis icositetrachoric tegum
ConjugateNone
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryF4×A1, order 2304
ConvexYes
NatureTame

The truncated icositetrachoric prism or ticope is a prismatic uniform polyteron that consists of 2 truncated icositetrachora, 24 truncated octahedral prisms, and 24 tesseracts. 1 truncated icositetrachoron, 1 tesseract, and 3 truncated octahedral prisms join at each vertex. As the name suggests, it is a prism based on the truncated icositetrachoron, which also makes it a convex segmentoteron.

This polyteron can be alternated into a snub disicositetrachoric antiprism, although it cannot be made uniform.

Vertex coordinates[edit | edit source]

The vertices of a truncated icositetrachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:

External links[edit | edit source]