# Triangular-antitegmatic hexacontatetrachoron

(Redirected from Square duoexpandotegum)
Triangular-antitegmatic hexacontatetrachoron
Rank4
TypeUniform dual
Notation
Coxeter diagramm4o3o3m ()
Elements
Cells64 triangular antitegums
Faces96+96 kites
Edges48+64+96
Vertices8+24+16+32
Vertex figure32 triangular bipyramids, 16 tetrahedra, 8+24 octahedra
Measures (edge length 1)
Dichoral angle${\displaystyle \arccos \left(-{\frac {4+{\sqrt {2}}}{7}}\right)\approx 140.66554^{\circ }}$
Central density1
Related polytopes
Abstract & topological properties
Flag count3072
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexYes
NatureTame

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 ${\displaystyle 3-{\sqrt {2}}\approx 1.58579}$, the icositetrachoron has edge length ${\displaystyle {\frac {3{\sqrt {2}}-2}{2}}\approx 1.12132}$, and the rectified tesseract has edge length ${\displaystyle {\frac {5{\sqrt {2}}-1}{7}}\approx 0.86730}$.