Icosayotton

Icosayotton
(OFF file)
Rank	9
Type	Uniform
Notation
Bowers style acronym	Icoy
Coxeter diagram	o3o3o3o3x3o3o3o3o ()
Elements
Yotta	20 trirectified 8-simplices
Zetta	90 birectified 7-simplices 90 trirectified 7-simplices
Exa	240 rectified 6-simplices 720 birectified 6-simplices
Peta	420 5-simplices 1680 rectified 5-simplices 1260 birectified 5-simplices
Tera	2520 pentachora 5040 rectified pentachora
Cells	6300 tetrahedra 4200 octahedra
Faces	8400 triangles
Edges	3150
Vertices	252
Vertex figure	Pentachoric duoprism, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {5}}{2}}\approx 1.11803$
Inradius	${\frac {\sqrt {5}}{6}}\approx 0.37268$
Hypervolume	${\frac {15619{\sqrt {5}}}{580608}}\approx 0.060153$
Diyottal angles	Trene–he–trene: $\arccos \left(-{\frac {1}{9}}\right)\approx 96.37937^{\circ }$
	Trene–broc–trene: $\arccos \left({\frac {1}{9}}\right)\approx 83.62063^{\circ }$
Height	${\frac {\sqrt {5}}{3}}\approx 0.74536$
Central density	1
Number of external pieces	20
Level of complexity	35
Related polytopes
Army	Icoy
Regiment	Icoy
Conjugate	None
Abstract & topological properties
Flag count	254016000
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A9×2, order 7257600
Flag orbits	35
Convex	Yes
Nature	Tame

The quadrirectified 9-simplex, also called the quadrirectified decayotton, icosayotton, or icoy, is a convex noble uniform 9-polytope. It consists of 20 trirectified 8-simplices. 10 trirectified 8-simplices join at each pentachoric duoprismatic vertex. As the name suggests, it is the quadrirectification of the 9-simplex, the medial stage of truncation between an 9-simplex and the dual 9-simplex.

It is also a convex segmentoyotton, as trirectified 8-simplex atop inverted trirectified 8-simplex.

Vertex coordinates

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

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

Representations

An icosayotton has the following Coxeter diagrams:

• o3o3o3o3x3o3o3o3o () (full symmetry)
• oo3oo3oo3xo3ox3oo3oo3oo&#x (A₈ axial, trirectified enneazetton atop alternate trirectified enneazetton)

Gallery

• 

  A₈ orthographic projection

• 

  A₇

• 

  A₆

• 

  A₅

• 

  A₄

• 

  A₃

• 

  A₂

External links

• Klitzing, Richard. "icoy".
• Wikipedia contributors. "Quadrirectified 9-simplex".