Rank5
TypeUniform
Notation
Bowers style acronymTahp
Coxeter diagramx o4x3x3o ()
Elements
Tera16 truncated tetrahedral prisms, 8 truncated octahedral prisms, 2 tesseractihexadecachora
Cells32 triangular prisms, 24 cubes, 64 hexagonal prisms, 32 truncated tetrahedra, 16 truncated octahedra
Faces64 triangles, 48+96+96 squares, 128 hexagons
Edges96+192+192
Vertices192
Vertex figureDigonal disphenoidal pyramid, edge lengths 1, 2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {19}}{2}}\approx 2.17945}$
Hypervolume${\displaystyle {\frac {307}{6}}\approx 51.16667}$
Diteral anglesTope–hip–tuttip: 120°
Tuttip–trip–tuttip: 120°
Tope–cube–tope: 90°
Tah–toe–tope: 90°
Tah–tut–tuttip: 90°
Height1
Central density1
Number of external pieces26
Level of complexity30
Related polytopes
ArmyTahp
RegimentTahp
DualDisphenoidal enneacontahexachoric tegum
ConjugateNone
Abstract & topological properties
Flag count23040
Euler characteristic2
OrientableYes
Properties
SymmetryB4×A1, order 768
ConvexYes
NatureTame

The tesseractihexadecachoric prism or tahp is a prismatic uniform polyteron that consists of 2 tesseractihexadecachora, 8 truncated octahedral prisms, and 16 truncated tetrahedral prisms. 1 tesseractihexadecachoron, 2 truncated octahedral prisms, and 2 truncated tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on the tesseractihexadecachoron, which also makes it a convex segmentoteron.

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\sqrt {2}},\,\pm {\sqrt {2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm {\frac {1}{2}}\right)}$.