# Sphenoverted tesseractitesseractihexadecachoron

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Sphenoverted tesseractitesseractihexadecachoron
Rank4
TypeUniform
Notation
Bowers style acronymWavitoth
Coxeter diagramo3x3o4x4/3*b ()
Elements
Cells16 octahedra, 8 quasitruncated hexahedra, 8 great cubicuboctahedra
Faces64+64 triangles, 24 squares, 48 octagrams
Edges96+192
Vertices96
Vertex figureWedge, edge lengths 1 (base square), 2 (top edge), and 2–2 (side edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2-{\sqrt {2}}}}\approx 0.76537}$
Hypervolume${\displaystyle {\frac {28-17{\sqrt {2}}}{3}}\approx 1.31946}$
Dichoral anglesOct–3–quith: 120°
Gocco–8/3–quith: 90°
Gocco–4–gocco: 90°
Gocco–3–oct: 60°
Related polytopes
ArmySrit, edge length ${\displaystyle {\sqrt {2}}-1}$
RegimentWavitoth
ConjugateRetrosphenoverted tesseractitesseractihexadecachoron
Convex coreSemi-uniform tesseractihexadecachoron
Abstract & topological properties
Flag count3456
Euler characteristic–24
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The sphenoverted tesseractitesseractihexadecachoron, or wavitoth, is a nonconvex uniform polychoron that consists of 16 regular octahedra, 8 quasitruncated hexahedra, and 8 great cubicuboctahedra. 1 octahedron, 2 quasitruncated hexahedra, and 2 great cubicuboctahedra join at each vertex.

The sphenoverted tesseractitesseractihexadecachoron can be vertex-inscribed into a great distetracontoctachoron and contains the vertices of an octagrammic duoprism and the quasitruncated hexahedral prism.

## Vertex coordinates

The vertices of a sphenoverted tesseractitesseractihexadecachoron of edge length 1 are given by all permutations of:

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

## Related polychora

The sphenoverted tesseractitesseractihexadecachoron is the colonel of a 7-member regiment. Its other members include the quasirhombated tesseract, great rhombic disoctachoron, great pseudorhombic prismatotesseract, grand quasirhombic prismatotesseract, disprismatointercepted tesseractihexadecachoron, and prismatointercepted tesseractitesseractihexadecachoron.