# Tesseractihemioctachoron

Tesseractihemioctachoron
Rank4
TypeUniform
Notation
Bowers style acronymTho
Coxeter diagram(x3o3o3o3/2*1)/2 ( /2)
Elements
Cells8 tetrahedra, 4 octahedra
Faces32 triangles
Edges24
Vertices8
Vertex figureTetrahemihexahedron, edge length 1
Edge figuretet 3 oct 3 tet 3 oct 3
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Dichoral angle60°
Number of external pieces40
Level of complexity5
Related polytopes
ArmyHex
RegimentHex
CompanyHex
DualTesseractihemioctacron
ConjugateNone
Abstract & topological properties
b01
b10
b23
b30
Flag count384
Euler characteristic4
OrientableNo
Properties
SymmetryD4, order 192
Flag orbits2
ConvexNo
NatureTame

The tesseractihemioctachoron, or tho, is a uniform hemipolychoron. It has 8 regular tetrahedra and 4 central octahedra as cells, with 4 tetrahedra and 3 octahedra at each vertex in the form of a tetrahemihexahedron. It is the 4D demicross.

It is a faceting of the hexadecachoron, analogous to how the tetrahemihexahedron is a faceting of the octahedron. It shares the hexadecachoron's vertices, edges, and faces. The 8 tetrahedra are half of those of the hexadecachoron, while the octahedra are its original vertex figures.

Notably, as well as being isogonal, the tesseractihemioctachoron is also edge- and face-transitive. It is one of only four non-regular uniform polychora to be vertex, edge, and face transitive.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the hexadecachoron.