Birectified 9-simplex

Birectified 9-simplex
Rank	9
Type	Uniform
Notation
Bowers style acronym	Breday
Coxeter diagram	o3o3x3o3o3o3o3o3o ()
Elements
Yotta	10 rectified 8-simplices 10 birectified 8-simplices
Zetta	45 7-simplices 90 rectified 7-simplices 45 birectified 7-simplices
Exa	360 6-simplices 360 rectified 6-simplices 120 birectified 6-simplices
Peta	1260 5-simplices 840 rectified 5-simplices 210 birectified 5-simplices
Tera	2520 pentachora 252+1260 rectified pentachora
Cells	210+3150 tetrahedra 1260 octahedra
Faces	840+2520 triangles
Edges	1260
Vertices	120
Vertex figure	Triangular-heptapetic duoprism, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {105}}{10}}\approx 1.02470$
Hypervolume	${\frac {913{\sqrt {5}}}{362880}}\approx 0.0056259$
Diyottal angles	Brene–roc–rene: $\arccos \left(-{\frac {1}{9}}\right)\approx 96.38037^{\circ }$
	Brene–broc–brene: $\arccos \left({\frac {1}{9}}\right)\approx 83.62063^{\circ }$
	Rene–oca–rene: $\arccos \left({\frac {1}{9}}\right)\approx 83.62063^{\circ }$
Height	${\frac {\sqrt {5}}{3}}\approx 0.74536$
Central density	1
Number of external pieces	20
Level of complexity	28
Related polytopes
Army	Breday
Regiment	Breday
Conjugate	None
Abstract & topological properties
Flag count	101606400
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A9, order 3628800
Flag orbits	28
Convex	Yes
Nature	Tame

The birectified 9-simplex, also called the birectified decayotton, or breday, is a convex uniform 9-polytope. It consists of 10 rectified 8-simplices and 10 birectified 8-simplices. 3 rectified 8-simplices and 7 birectified 8-simplices join at each triangular-heptapetic duoprismatic vertex. As the name suggests, it is the birectification of the 9-simplex.

It is also a convex segmentoyotton, as rectified 8-simplex atop birectified 8-simplex.

Vertex coordinates

The vertices of a birectified 9-simplex of edge length 1 can be given in ten dimensions as all permutations of:

• $\left({\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,0,\,0,\,0,\,0,\,0,\,0,\,0\right)$.

External links

• Klitzing, Richard. "breday".
• Wikipedia contributors. "Birectified 9-simplex".