Square-hexadecachoric duoprism

Square-hexadecachoric duoprism
Rank	6
Type	Uniform
Notation
Bowers style acronym	Squahex
Coxeter diagram	x4o o4o3o3x ()
Bracket notation	[<IIII>II]
Elements
Peta	16 square-tetrahedral duoprisms, 4 hexadecachoric prisms
Tera	64 tetrahedral prisms, 32 triangular-square duoprisms, 4 hexadecachora
Cells	464 tetrahedra, 128 triangular prisms, 24 cubes
Faces	128 triangles, 8+96 squares
Edges	32+96
Vertices	32
Vertex figure	Octahedral scalene, edge lengths 1 (base octahedron) and √2 (top and side edges)
Measures (edge length 1)
Circumradius	1
Hypervolume	${\frac {1}{6}}\approx 0.16667$
Dipetal angles	Squatet–tisdip–squatet: 120°
	Hexip–tepe–squatet: 90°
	Hexip–hex–hexip: 90°
Heights	Hexip atop hexip: 1
	Squatet atop tet-dual squatet: ${\frac {\sqrt {2}}{2}}\approx 0.70711$
Central density	1
Number of external pieces	20
Level of complexity	15
Related polytopes
Army	Squahex
Regiment	Squahex
Dual	Square-tesseractic duotegum
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4×B2, order 3072
Convex	Yes
Nature	Tame

The square-hexadecachoric duoprism or squahex is a convex uniform duoprism that consists of 4 hexadecachoric prisms and 16 square-tetrahedral duoprisms. Each vertex joins 2 hexadecachoric prisms and 8 square-tetrahedral duoprisms. It is a duoprism based on a square and a hexadecachoron, which makes it a convex segmentopeton

The square-hexadecachoric duoprism can be vertex-inscribed into the rectified hexacontatetrapeton.

Vertex coordinates

The vertices of a square-hexadecachoric duoprism of edge length 1 are given by all permutations and sign changes of the last four coordinates of:

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

Representations

A square-hexadecachoric duoprism has the following Coxeter diagrams:

• x4o o4o3o3x (full symmetry)
• x4o x3o3o *d3o (D4×B2 symmetry, hexadecachoron as demitesseract)
• x x o4o3o3x (B4×A1×A1 symmetry, square as rectangle)
• x x x3o3o *d3o (D4×A1×A1 symmetry, both components in half symmetry)

External links

• Klitzing, Richard. "squahex".