Rank4
TypeUniform
Notation
Bowers style acronymThatpath
Coxeter diagramx3x3x4/3x4*b ()
Elements
Cells24 octagrammic prisms, 16 truncated octahedra, 8 great rhombicuboctahedra, 8 cuboctatruncated cuboctahedra
Faces96+96 squares, 64+64 hexagons, 48 octagons, 48 octagrams
Edges192+192+192+192
Vertices384
Vertex figureIrregular tetrahedron, edge lengths 2 (2), 3 (2), 2+2 (1), and 2–2 (1)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {4+{\sqrt {2}}}}\approx 2.32685}$
Hypervolume${\displaystyle 6\left(7+12{\sqrt {2}}\right)\approx 143.82338}$
Dichoral anglesCotco–8/3–stop: 135°
Toe–4–stop: 135°
Cotco–6–toe: 120°
Cotco–8–girco: 90°
Girco–4–stop: 90°
Toe–6–girco: 60°
Number of external pieces176
Level of complexity60
Related polytopes
ArmySemi-uniform Gidpith, edge lengths ${\displaystyle {\sqrt {2}}-1}$ (octagons), 1 (bases of hexagonal prisms)
RegimentThatpath
Convex coreTesseract
Abstract & topological properties
Flag count9216
Euler characteristic–24
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The tesseractihexadecatruncated prismatotesseractihexadecachoron, or thatpath, is a nonconvex uniform polychoron that consists of 24 octagrammic prisms, 16 truncated octahedra, 8 great rhombicuboctahedra, and 8 cuboctatruncated cuboctahedra. 1 of each type of cell join at each vertex.

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