Partially-expanded demihexeract

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Partially-expanded demihexeract
File:Partially-expanded demihexeract.png
Rank6
TypeScaliform
Notation
Bowers style acronymPexhax
Coxeter diagram
Elements
Peta6 partially-expanded demipenteracts, 6 demipenteracts, 8 triangular-tetrahedral duoprisms, 12 hexadecachoric prisms, 32 partially-expanded hexatera
Tera12 truncated tetrahedral cupoliprisms, 24+72+96 tetrahedral prisms, 24+36 hexadecachora, 32 triangular duoprisms, 96 triangular cupofastegiums, 96 pentachora
Cells8 truncated tetrahedra, 48+96+288 triangular prisms, 96 triangular cupolas, 24+72+144+192+288 tetrahedra
Faces32 hexagons, 144+144 squares, 32+96+288+576 triangles
Edges48+96+144+288
Vertices96
Measures (edge length 1)
Circumradius
Central density1
Related polytopes
DualTetrahedral-triakis tetrahedral duoaltertegum
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3×B3/2, order 1152
ConvexYes
NatureTame

The partially-expanded demihexeract or pexhax, also known as the tetrahedral-truncated tetrahedral duoalterprism, is a convex scaliform polypeton that consists of 6 partially-expanded demipenteracts, 6 demipenteracts, 8 triangular-tetrahedral duoprisms, 12 hexadecachoric prisms, and 32 partially-expanded hexatera formed by tetrahedrally alternating the cubic-small rhombicuboctahedral duoprism.

It can also be obtained as a Stott expansion of the demihexeract, or as the convex hull of 2 opposite tetrahedral-truncated tetrahedral duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a partially-expanded demihexeract of edge length 1, are given by all permutations and even changes of sign of the first and last three coordinates of:

Representations[edit | edit source]

- - xo3xx3ox xo3oo3ox&#zx

External links[edit | edit source]