Tridiminished icosiheptaheptacontadipeton

Tridiminished icosiheptaheptacontadipeton
File:Tridiminished icosiheptaheptacontadipeton.png (OFF file)
Rank	6
Type	Scaliform
Notation
Bowers style acronym	Tedjak
Coxeter diagram	xoo3ooo3oxo *b3oox&#x
Elements
Peta	24 hexatera, 24 hexadecachoric pyramids, 3 demipenteracts
Tera	48+96+144 pentachora, 3+24 hexadecachora
Cells	48+72+192+288 tetrahedra
Faces	96+96+288 triangles
Edges	72+96
Vertices	24
Vertex figure	Bidiminished demipenteract, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {6}}{3}}\approx 0.81650$
Central density	1
Related polytopes
Army	Tedjak
Regiment	Tedjak
Dual	Tesseractic triorthonotch
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4÷B4, order 1152
Convex	Yes
Nature	Tame

The tridiminished icosiheptaheptacontadipeton, or tedjak, also known as the hexadecachoric gyrotrigonism or hexadecachoric triorthowedge, is a convex scaliform polypeton that consists of 3 demipenteracts, 24 hexadecachoric pyramids, and 24 hexatera. Two demipenteracts, nine hexadecachoric pyramids, and six hexatera meet at its 24 bidiminished demipenteractic vertices.

As the name suggests, it can be obtained by removing 3 vertices from the icosiheptaheptacontadipeton, specifically 3 vertices forming an equilateral triangle of edge length ${\sqrt {2}}$. Each diminishing reveals one demipenteractic facet, while removing some of the hexateron facets entirely. All the hexadecachoric pyramid facets correspond to triacontaditera in the full icosiheptaheptacontadipeton.

It is also a quotient prism based on the stellated icositetrachoron.

Vertex coordinates

The vertices of a tridiminished icosiheptaheptacontadipeton of edge length 1 are given by all permutations and even sign changes of the first four coordinates of:

• $\left(0,\,0,\,0,\,{\frac {\sqrt {2}}{2}},\,0,\,{\frac {\sqrt {6}}{6}}\right),$
• $\left({\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {6}}{12}}\right),$
• $\left({\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {6}}{12}}\right).$

External links

• Klitzing, Richard. "tedjak".