Small rhombated demitesseract

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Small rhombated demitesseract
Rank4
TypeSemi-uniform
Notation
Coxeter diagramx3o3o *b3y
Elements
Cells8+8 tetrahedra, 8 rhombitetratetrahedra
Faces32+32 triangles, 24 rectangles
Edges48+48
Vertices32
Vertex figureTriangular frustum
Measures (edge lengths a, b)
Circumradius
Hypervolume
Dichoral anglesRatet–3–tet: 120°
 Ratet–4–ratet: 90°
Central density1
Related polytopes
DualTriangular-tegmatic triacontadichoron
ConjugateSmall rhombated demitesseract
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryD4, order 192
ConvexYes
NatureTame

The small rhombated demitesseract or runcic tesseract is a convex semi-uniform polychoron that is a variant of the rectified tesseract with demitesseractic symmetry. As such it can be represented by x3o3o *b3y, and has 16 tetrahedra (of two types, sizes x and y) and 8 rhombitetrahedra (type x3o3y) as cells, with two edge lengths.

Vertex coordinates[edit | edit source]

A small rhombated demitesseract with edge lengths a and b has vertices given by all permutations and even sign changes of:

Alternative coordinates in a different orientation can be given by all even sign changes and permutations of: