# Transitional bicantitruncatodecachoron

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Transitional bicantitruncatodecachoron
File:Transitional bicantitruncatodecachoron.png
Rank4
TypeIsogonal
Notation
Bowers style acronymTabcated
Coxeter diagramao3bc3cb3oa&#zd (c = b+a/2)
Elements
Cells20 ditrigonal trapezoprisms, 20 triangular trapezorhombihedra, 10 truncated tetrahedra
Faces40 triangles, 120 isosceles trapezoids, 30 squares 40 ditrigons
Edges60+120+120
Vertices120
Vertex figureIsosceles trapezoidal pyramid
Measures (edge length 1)
Central density1
Related polytopes
ArmyTabcated
RegimentTabcated
DualTransitional bimetadecachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA4×2, order 240
ConvexYes
NatureTame

The transitional bicantitruncatodecachoron or tabcated is a convex isogonal polychoron that consists of 10 truncated tetrahedra, 20 ditrigonal trapezoprisms, and 20 triangular trapezorhombihedra. 1 truncated tetrahedron, 2 ditrigonal trapezoprisms, and 2 triangular trapezorhombihedra join at each vertex.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the great rhombated pentachoron, where if the great rhombated pentachora are of the form a3b3c3o, then c = b+a/2. It is one of five polychora (including two transitional cases) formed from two great rhombated pentachora, and is the transitional point between the small bicantitruncatodecachoron and medial bicantitruncatodecachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\displaystyle {\frac {2+{\sqrt {2}}}{2}}}$ ≈ 1:1.70711.