 Rank4
TypeUniform
SpaceSpherical
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$\sqrt{4+\sqrt2} ≈ 2.32685$ Hypervolume$6\left(7+12\sqrt2\right) ≈ 143.82338$ 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
RegimentThatpath
Convex coreTesseract
Abstract & topological properties
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.

• $\left(±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$ 