Triangular-antitegmatic hexacontatetrachoron

Triangular-antitegmatic hexacontatetrachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m4o3o3m ()
Elements
Cells	64 triangular antitegums
Faces	96+96 kites
Edges	48+64+96
Vertices	8+24+16+32
Vertex figure	32 triangular bipyramids, 16 tetrahedra, 8+24 octahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {4+{\sqrt {2}}}{7}}\right)\approx 140.66554^{\circ }$
Central density	1
Related polytopes
Dual	Small disprismatotesseracti-hexadecachoron
Abstract & topological properties
Flag count	3072
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

The triangular-antitegmatic hexacontatetrachoron or square duoexpandotegum is a convex isochoric polychoron with 64 triangular antitegums as cells. It can be obtained as the dual of the small disprismatotesseractihexadecachoron.

It is the square member of the infinite family of isochoric duoexpandotegums.

It can also be constructed as the convex hull of a tesseract, a hexadecachoron, an icositetrachoron (as a rectified hexadecachoron), and a rectified tesseract. If the tesseract has edge length 1, the hexadecachoron has edge length $3-{\sqrt {2}}\approx 1.58579$, the icositetrachoron has edge length ${\frac {3{\sqrt {2}}-2}{2}}\approx 1.12132$, and the rectified tesseract has edge length ${\frac {5{\sqrt {2}}-1}{7}}\approx 0.86730$.

External links

• Klitzing, Richard. "m3o3o4m".
• Quickfur. "The Triangular Antitegmatic Hexacontatetrachoron".