Pentistericantitruncated 6-simplex

Pentistericantitruncated 6-simplex
Rank	6
Type	Uniform
Notation
Bowers style acronym	Tacogral
Coxeter diagram	x3x3x3o3x3x ()
Elements
Peta	7 stericantitruncated 5-simplices ; 7 steriruncitruncated 5-simplices ; 21 prismatorhombated pentachoric prisms ; 21 great rhombated pentachoric prisms ; 35 hexagonal-truncated tetrahedral duoprisms ; 35 hexagonal-truncated octahedral duoprisms
Tera	210 triangular-square duoprisms ; 140 triangular-hexagonal duoprisms ; 210 square-hexagonal duoprisms ; 105+105+105 truncated tetrahedral prisms ; 140+140 hexagonal duoprisms ; 105 cuboctahedral prisms ; 105+105 truncated octahedral prisms ; 42+42 prismatorhombated pentachora ; 42 great rhombated pentachora
Cells	420+420+420+420 triangular prisms ; 420+420+420+420+420+420+210 hexagonal prisms ; 630+630 cubes ; 210+210 truncated tetrahedra ; 210 cuboctahedra ; 210 truncated octahedra
Faces	840+840 triangles ; 1260+1260+1260+1260+1260+630+630 squares ; 840+840+420 hexagons
Edges	2520+2520+1260+1260+1260
Vertices	2520
Vertex figure	Irregular square tettene
Measures (edge length 1)
Circumradius
Hypervolume
Central density	1
Related polytopes
Army	Tacogral
Regiment	Tacogral
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A6, order 5040
Convex	Yes
Nature	Tame

The pentistericantitruncated 6-simplex, also called the pentistericantitruncated heptapeton, tericelligreatorhombated heptapeton, or tacogral, is a convex uniform 6-polytope. It consists of 7 stericantitruncated 5-simplices, 7 steriruncitruncated 5-simplices, 21 prismatorhombated pentachoric prisms, 21 great rhombated pentachoric prisms, 35 hexagonal-truncated tetrahedral duoprisms, and 35 hexagonal-truncated octahedral duoprisms. 1 stericantitruncated 5-simplex, 1 steriruncitruncated 5-simplex, 1 prismatorhombated pentachoric prism, 1 great rhombated pentachoric prism, 1 hexagonal-truncated tetrahedral duoprism, and 2 hexagonal-truncated octahedral duoprisms join at each vertex. As the name suggests, it is the pentistericantitruncation of the 6-simplex.

Gallery[edit | edit source]

A₅ orthographic projection
A₄
A₃
A₂

External links[edit | edit source]

Klitzing, Richard. "tacogral".
Wikipedia contributors. "Pentistericantitruncated 6-simplex".

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v t e truncations
Name	OBSA	Schläfli symbol	CD diagram	Image
6-simplex	hop	${3,3,3,3,3}$
Rectified 6-simplex	ril	r ${3,3,3,3,3}$
Birectified 6-simplex	bril	t₂ ${3,3,3,3,3}$
Truncated 6-simplex	til	t ${3,3,3,3,3}$
Cantellated 6-simplex	sril	rr ${3,3,3,3,3}$
Runcinated 6-simplex	spil	t_0,3 ${3,3,3,3,3}$
Stericated 6-simplex	scal	t_0,4 ${3,3,3,3,3}$
Pentellated 6-simplex	staf	t_0,5 ${3,3,3,3,3}$
Bitruncated 6-simplex	batal	t_1,2 ${3,3,3,3,3}$
Bicantellated 6-simplex	sabril	t_1,3 ${3,3,3,3,3}$
Biruncinated 6-simplex	sibpof	t_1,4 ${3,3,3,3,3}$
Tritruncated 6-simplex	fe	t_2,3 ${3,3,3,3,3}$
Cantitruncated 6-simplex	gril	tr ${3,3,3,3,3}$
Runcitruncated 6-simplex	patal	t_0,1,3 ${3,3,3,3,3}$
Steritruncated 6-simplex	catal	t_0,1,4 ${3,3,3,3,3}$
Pentitruncated 6-simplex	tocal	t_0,1,5 ${3,3,3,3,3}$
Runcicantellated 6-simplex	pril	t_0,2,3 ${3,3,3,3,3}$
Stericantellated 6-simplex	cral	t_0,2,4 ${3,3,3,3,3}$
Penticantellated 6-simplex	topal	t_0,2,5 ${3,3,3,3,3}$
Steriruncinated 6-simplex	copal	t_0,3,4 ${3,3,3,3,3}$
Bicantitruncated 6-simplex	gabril	t_1,2,3 ${3,3,3,3,3}$
Biruncitruncated 6-simplex	bapril	t_1,2,4 ${3,3,3,3,3}$
Runcicantitruncated 6-simplex	gapil	t_0,1,2,3 ${3,3,3,3,3}$
Stericantitruncated 6-simplex	cagral	t_0,1,2,4 ${3,3,3,3,3}$
Penticantitruncated 6-simplex	togral	t_0,1,2,5 ${3,3,3,3,3}$
Steriruncitruncated 6-simplex	captal	t_0,1,3,4 ${3,3,3,3,3}$
Pentiruncitruncated 6-simplex	tocral	t_0,1,3,5 ${3,3,3,3,3}$
Pentisteritruncated 6-simplex	tactaf	t_0,1,4,5 ${3,3,3,3,3}$
Steriruncicantellated 6-simplex	copril	t_0,2,3,4 ${3,3,3,3,3}$
Pentiruncicantellated 6-simplex	taporf	t_0,2,3,5 ${3,3,3,3,3}$
Biruncicantitruncated 6-simplex	gibpof	t_1,2,3,4 ${3,3,3,3,3}$
Steriruncicantitruncated 6-simplex	gacal	t_0,1,2,3,4 ${3,3,3,3,3}$
Pentiruncicantitruncated 6-simplex	tagopal	t_0,1,2,3,5 ${3,3,3,3,3}$
Pentistericantitruncated 6-simplex	tacogral	t_0,1,2,4,5 ${3,3,3,3,3}$
Omnitruncated 6-simplex	gotaf	t_0,1,2,3,4,5 ${3,3,3,3,3}$

Pentistericantitruncated 6-simplex

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External links[edit | edit source]

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