Sphenoverted tesseractitesseractihexadecachoron

Sphenoverted tesseractitesseractihexadecachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Wavitoth
Coxeter diagram	o3x3o4x4/3*b ()
Elements
Cells	16 octahedra, 8 quasitruncated hexahedra, 8 great cubicuboctahedra
Faces	64+64 triangles, 24 squares, 48 octagrams
Edges	96+192
Vertices	96
Vertex figure	Wedge, edge lengths 1 (base square), √2 (top edge), and √2–√2 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {2-{\sqrt {2}}}}\approx 0.76537$
Hypervolume	${\frac {28-17{\sqrt {2}}}{3}}\approx 1.31946$
Dichoral angles	Oct–3–quith: 120°
	Gocco–8/3–quith: 90°
	Gocco–4–gocco: 90°
	Gocco–3–oct: 60°
Related polytopes
Army	Srit, edge length ${\sqrt {2}}-1$
Regiment	Wavitoth
Conjugate	Retrosphenoverted tesseractitesseractihexadecachoron
Convex core	Semi-uniform tesseractihexadecachoron
Abstract & topological properties
Flag count	3456
Euler characteristic	–24
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

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.

Gallery

Vertex coordinates

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

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

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.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#221).

• Klitzing, Richard. "wavitoth".