Partially-expanded demipenteract

Partially-expanded demipenteract
(OFF file)
Rank	5
Type	Scaliform
Notation
Bowers style acronym	Pexhin
Coxeter diagram
Elements
Tera	12 tetrahedral prisms, 16 triangular cupofastegiums, 6 hexadecachora, 4 truncated tetrahedral alterprisms
Cells	24+24+48 tetrahedra, 8+48 triangular prisms, 32 triangular cupolas, 4 truncated tetrahedra
Faces	16+96+96 triangles, 24+48 squares, 16 hexagons
Edges	24+24+48+96
Vertices	48
Vertex figure	Digonal-octahedral orthowedge, edge lengths 1 (including base octahedron), √2, √3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {26}}{4}}\approx 1.27475$
Hypervolume	${\frac {173{\sqrt {2}}}{120}}\approx 2.03882$
Height	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Central density	1
Related polytopes
Army	Pexhin
Regiment	Pexhin
Dual	Digonal-triakis tetrahedral duoaltertegum
Conjugate	Partially expanded demipenteract
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(B2×(A3×2))/2, order 192
Convex	Yes
Nature	Tame

The partially-expanded demipenteract or pexhin, also known as the truncated tetrahedral altersquarism, tutas, or digonal-truncated tetrahedral duoalterprism, is a convex scaliform polyteron that consists of 4 truncated tetrahedral alterprisms, 6 hexadecachora, 16 triangular cupofastegiums, and 12 tetrahedral prisms. 1 hexadecachoron, 2 truncated tetrahedral alterprisms, 2 tetrahedral prisms, and 4 trianguar cupofastegiums join at each vertex. It can be formed by tetrahedrally alternating the square-small rhombicuboctahedral duoprism, so that all the small rhombicuboctahedra turn into truncated tetrahedra.

The partially-expanded demipenteract can be vertex-inscribed into a small prismated demipenteract.

It can also be obtained as a Stott expansion of the demipenteract.

Vertex coordinates

The vertices of a partially-expanded demipenteract of edge length 1 are given by:

• $\left({\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {3{\sqrt {2}}}{4}},\,0,\,\pm {\frac {1}{2}}\right),$

with all permutations and even changes of sign of the first three coordinates, and

• $\left({\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {3{\sqrt {2}}}{4}},\,\pm {\frac {1}{2}},\,0\right),$

with all permutations and odd changes of sign of the first three coordinates.

External links

• Klitzing, Richard. "pexhin".