Pentellated 6-simplexes

6-simplex	Pentellated 6-simplex	Pentitruncated 6-simplex	Penticantellated 6-simplex
Penticantitruncated 6-simplex	Pentiruncitruncated 6-simplex	Pentiruncicantellated 6-simplex	Pentiruncicantitruncated 6-simplex
Pentisteritruncated 6-simplex	Pentistericantitruncated 6-simplex	Pentisteriruncicantitruncated 6-simplex (Omnitruncated 6-simplex)
Orthogonal projections in A6 Coxeter plane

In six-dimensional geometry, a pentellated 6-simplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-simplex.

There are unique 10 degrees of pentellations of the 6-simplex with permutations of truncations, cantellations, runcinations, and sterications. The simple pentellated 6-simplex is also called an expanded 6-simplex, constructed by an expansion operation applied to the regular 6-simplex. The highest form, the pentisteriruncicantitruncated 6-simplex, is called an omnitruncated 6-simplex with all of the nodes ringed.

Pentellated 6-simplex

Pentellated 6-simplex
Type	Uniform 6-polytope
Schläfli symbol	t0,5{3,3,3,3,3}
Coxeter-Dynkin diagram
5-faces	126: 7+7 {3^4}   21+21 {}×{3,3,3} 35+35 {3}×{3,3}
4-faces	434
Cells	630
Faces	490
Edges	210
Vertices	42
Vertex figure	5-cell antiprism
Coxeter group	A6×2, [[3,3,3,3,3]], order 10080
Properties	convex

Alternate names

• Expanded 6-simplex
• Small terated tetradecapeton (Acronym: staf) (Jonathan Bowers)^[1]

Cross-sections

The maximal cross-section of the pentellated 6-simplex with a 5-dimensional hyperplane is a stericated hexateron. This cross-section divides the pentellated 6-simplex into two hexateral hypercupolas consisting of 7 5-simplexes, 21 5-cell prisms and 35 Tetrahedral-Triangular duoprisms each.

Coordinates

The vertices of the pentellated 6-simplex can be positioned in 7-space as permutations of (0,1,1,1,1,1,2). This construction is based on facets of the pentellated 7-orthoplex.

A second construction in 7-space, from the center of a rectified 7-orthoplex is given by coordinate permutations of:

(1,-1,0,0,0,0,0)

Root vectors

Its 42 vertices represent the root vectors of the simple Lie group A₆. It is the vertex figure of the 6-simplex honeycomb.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Symmetry	[[7]]^(*)=[14]	[6]	[[5]]^(*)=[10]
Ak Coxeter plane	A3	A2
Graph
Symmetry	[4]	[[3]]^(*)=[6]

Note: (*) Symmetry doubled for A_k graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram.

Configuration

This configuration matrix represents the expanded 6-simplex, with 12 permutations of elements. The rows and columns correspond to vertices, edges, faces, cells, 4-faces and 5-faces. The diagonal numbers say how many of each element occur in the whole polytope. The nondiagonal numbers say how many of the column's element occur in or at the row's element.^[2]

Element	fk	f0	f1	f2		f3		f4			f5
	f0	42	10	20	20	20	60	10	40	30	2	10	20
	f1	2	210	4	4	6	18	4	16	12	1	5	10
	f2	3	3	280	*	3	3	3	6	3	1	3	4
		4	4	*	210	0	6	0	6	6	0	2	6
	f3	4	6	4	0	210	*	2	2	0	1	2	1
		6	9	2	3	*	420	0	2	2	0	1	3
	f4	5	10	10	0	5	0	84	*	*	1	1	0
		8	16	8	6	2	4	*	210	*	0	1	1
		9	18	6	9	0	6	*	*	140	0	0	2
	f5	6	15	20	0	15	0	6	0	0	14	*	*
		10	25	20	10	10	10	2	5	0	*	42	*
		12	30	16	18	3	18	0	3	4	*	*	70

Pentitruncated 6-simplex

Pentitruncated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,1,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	826
Cells	1785
Faces	1820
Edges	945
Vertices	210
Vertex figure
Coxeter group	A6, [3,3,3,3,3], order 5040
Properties	convex

Alternate names

• Teracellated heptapeton (Acronym: tocal) (Jonathan Bowers)^[3]

Coordinates

The vertices of the runcitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,1,1,1,2,3). This construction is based on facets of the runcitruncated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Dihedral symmetry	[7]	[6]	[5]
Ak Coxeter plane	A3	A2
Graph
Dihedral symmetry	[4]	[3]

Penticantellated 6-simplex

Penticantellated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,2,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1246
Cells	3570
Faces	4340
Edges	2310
Vertices	420
Vertex figure
Coxeter group	A6, [3,3,3,3,3], order 5040
Properties	convex

Alternate names

• Teriprismated heptapeton (Acronym: topal) (Jonathan Bowers)^[4]

Coordinates

The vertices of the runcicantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,1,1,1,2,3). This construction is based on facets of the penticantellated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Dihedral symmetry	[7]	[6]	[5]
Ak Coxeter plane	A3	A2
Graph
Dihedral symmetry	[4]	[3]

Penticantitruncated 6-simplex

penticantitruncated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,1,2,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1351
Cells	4095
Faces	5390
Edges	3360
Vertices	840
Vertex figure
Coxeter group	A6, [3,3,3,3,3], order 5040
Properties	convex

Alternate names

• Terigreatorhombated heptapeton (Acronym: togral) (Jonathan Bowers)^[5]

Coordinates

The vertices of the penticantitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,1,1,2,3,4). This construction is based on facets of the penticantitruncated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Dihedral symmetry	[7]	[6]	[5]
Ak Coxeter plane	A3	A2
Graph
Dihedral symmetry	[4]	[3]

Pentiruncitruncated 6-simplex

pentiruncitruncated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,1,3,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1491
Cells	5565
Faces	8610
Edges	5670
Vertices	1260
Vertex figure
Coxeter group	A6, [3,3,3,3,3], order 5040
Properties	convex

Alternate names

• Tericellirhombated heptapeton (Acronym: tocral) (Jonathan Bowers)^[6]

Coordinates

The vertices of the pentiruncitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,1,1,2,3,4). This construction is based on facets of the pentiruncitruncated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Dihedral symmetry	[7]	[6]	[5]
Ak Coxeter plane	A3	A2
Graph
Dihedral symmetry	[4]	[3]

Pentiruncicantellated 6-simplex

Pentiruncicantellated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,2,3,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1596
Cells	5250
Faces	7560
Edges	5040
Vertices	1260
Vertex figure
Coxeter group	A6, [[3,3,3,3,3]], order 10080
Properties	convex

Alternate names

• Teriprismatorhombated tetradecapeton (Acronym: taporf) (Jonathan Bowers)^[7]

Coordinates

The vertices of the pentiruncicantellated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,1,2,3,3,4). This construction is based on facets of the pentiruncicantellated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Symmetry	[[7]]^(*)=[14]	[6]	[[5]]^(*)=[10]
Ak Coxeter plane	A3	A2
Graph
Symmetry	[4]	[[3]]^(*)=[6]

Note: (*) Symmetry doubled for A_k graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram.

Pentiruncicantitruncated 6-simplex

Pentiruncicantitruncated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,1,2,3,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1701
Cells	6825
Faces	11550
Edges	8820
Vertices	2520
Vertex figure
Coxeter group	A6, [3,3,3,3,3], order 5040
Properties	convex

Alternate names

• Terigreatoprismated heptapeton (Acronym: tagopal) (Jonathan Bowers)^[8]

Coordinates

The vertices of the pentiruncicantitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,1,2,3,4,5). This construction is based on facets of the pentiruncicantitruncated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Dihedral symmetry	[7]	[6]	[5]
Ak Coxeter plane	A3	A2
Graph
Dihedral symmetry	[4]	[3]

Pentisteritruncated 6-simplex

Pentisteritruncated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,1,4,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1176
Cells	3780
Faces	5250
Edges	3360
Vertices	840
Vertex figure
Coxeter group	A6, [[3,3,3,3,3]], order 10080
Properties	convex

Alternate names

• Tericellitruncated tetradecapeton (Acronym: tactaf) (Jonathan Bowers)^[9]

Coordinates

The vertices of the pentisteritruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,2,2,2,3,4). This construction is based on facets of the pentisteritruncated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Symmetry	[[7]]^(*)=[14]	[6]	[[5]]^(*)=[10]
Ak Coxeter plane	A3	A2
Graph
Symmetry	[4]	[[3]]^(*)=[6]

Note: (*) Symmetry doubled for A_k graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram.

Pentistericantitruncated 6-simplex

pentistericantitruncated 6-simplex
Type	uniform 6-polytope
Schläfli symbol	t0,1,2,4,5{3,3,3,3,3}
Coxeter-Dynkin diagrams
5-faces	126
4-faces	1596
Cells	6510
Faces	11340
Edges	8820
Vertices	2520
Vertex figure
Coxeter group	A6, [3,3,3,3,3], order 5040
Properties	convex

Alternate names

• Great teracellirhombated heptapeton (Acronym: gatocral) (Jonathan Bowers)^[10]

Coordinates

The vertices of the pentistericantittruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,2,2,3,4,5). This construction is based on facets of the pentistericantitruncated 7-orthoplex.

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Dihedral symmetry	[7]	[6]	[5]
Ak Coxeter plane	A3	A2
Graph
Dihedral symmetry	[4]	[3]

Omnitruncated 6-simplex

Omnitruncated 6-simplex
Type	Uniform 6-polytope
Schläfli symbol	t0,1,2,3,4,5{3^5}
Coxeter-Dynkin diagrams
5-faces	126: 14 t0,1,2,3,4{3^4}  42 {}×t0,1,2,3{3^3}  ×  70 {6}×t0,1,2{3,3}  ×
4-faces	1806
Cells	8400
Faces	16800: 4200 {6}   1260 {4}
Edges	15120
Vertices	5040
Vertex figure	irregular 5-simplex
Coxeter group	A6, [[3^5]], order 10080
Properties	convex, isogonal, zonotope

The omnitruncated 6-simplex has 5040 vertices, 15120 edges, 16800 faces (4200 hexagons and 1260 squares), 8400 cells, 1806 4-faces, and 126 5-faces. With 5040 vertices, it is the largest of 35 uniform 6-polytopes generated from the regular 6-simplex.

Alternate names

• Pentisteriruncicantitruncated 6-simplex (Johnson's omnitruncation for 6-polytopes)
• Omnitruncated heptapeton
• Great terated tetradecapeton (Acronym: gotaf) (Jonathan Bowers)^[11]

Permutohedron and related tessellation

The omnitruncated 6-simplex is the permutohedron of order 7. The omnitruncated 6-simplex is a zonotope, the Minkowski sum of seven line segments parallel to the seven lines through the origin and the seven vertices of the 6-simplex.

Like all uniform omnitruncated n-simplices, the omnitruncated 6-simplex can tessellate space by itself, in this case 6-dimensional space with three facets around each hypercell. It has Coxeter-Dynkin diagram of        .

Coordinates

The vertices of the omnitruncated 6-simplex can be most simply positioned in 7-space as permutations of (0,1,2,3,4,5,6). This construction is based on facets of the pentisteriruncicantitruncated 7-orthoplex, t_0,1,2,3,4,5{3⁵,4},              .

Images

orthographic projections

Ak Coxeter plane	A6	A5	A4
Graph
Symmetry	[[7]]^(*)=[14]	[6]	[[5]]^(*)=[10]
Ak Coxeter plane	A3	A2
Graph
Symmetry	[4]	[[3]]^(*)=[6]

Note: (*) Symmetry doubled for A_k graphs with even k due to symmetrically-ringed Coxeter-Dynkin diagram.

Configuration

This configuration matrix represents the omnitruncated 6-simplex, with 35 permutations of elements. The rows and columns correspond to vertices, edges, faces, cells, 4-faces and 5-faces. The diagonal numbers say how many of each element occur in the whole polytope. The nondiagonal numbers say how many of the column's element occur in or at the row's element.^[12]

Element	fk	f0	f1			f2									f3										f4									f5
	f0	5040	2	2	2	2	2	2	2	1	2	2	1	1	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	1	2	1	1	2	2	2
	f1	2	5040	*	*	1	1	1	1	1	0	0	0	0	1	1	1	2	1	1	2	1	0	0	1	1	2	1	2	1	1	1	0	1	2	2
		2	*	5040	*	1	0	0	1	0	1	1	1	0	1	1	2	1	0	1	0	1	1	2	1	2	1	2	1	1	1	0	1	2	1	2
		2	*	*	5040	0	1	1	0	0	1	1	0	1	1	1	0	0	2	1	1	1	2	1	2	1	1	1	1	0	2	1	1	2	2	1
	f2	6	3	3	0	1680	*	*	*	*	*	*	*	*	1	1	1	1	0	0	0	0	0	0	1	1	1	1	1	1	0	0	0	1	1	2
		4	2	0	2	*	2520	*	*	*	*	*	*	*	1	0	0	0	1	1	1	0	0	0	1	1	1	0	1	0	1	1	0	1	2	1
		4	2	0	2	*	*	2520	*	*	*	*	*	*	0	1	0	0	1	0	1	1	0	0	1	0	1	1	1	0	1	1	0	1	2	1
		4	2	2	0	*	*	*	2520	*	*	*	*	*	0	0	1	1	0	1	0	1	0	0	0	1	1	1	1	1	1	0	0	1	1	2
		4	4	0	0	*	*	*	*	1260	*	*	*	*	0	0	0	2	0	0	2	0	0	0	0	0	2	0	2	1	0	1	0	0	2	2
		6	0	3	3	*	*	*	*	*	1680	*	*	*	1	0	0	0	0	0	0	1	1	1	1	1	1	1	0	0	1	0	1	2	1	1
		4	0	2	2	*	*	*	*	*	*	2520	*	*	0	1	0	0	0	1	0	0	1	1	1	1	0	1	1	0	1	0	1	2	1	1
		4	0	4	0	*	*	*	*	*	*	*	1260	*	0	0	2	0	0	0	0	0	0	2	0	2	0	2	0	1	0	0	1	2	0	2
		6	0	0	6	*	*	*	*	*	*	*	*	840	0	0	0	0	2	0	0	0	2	0	2	0	0	0	0	0	2	1	1	2	2	0
	f3	24	12	12	12	4	6	0	0	0	4	0	0	0	420	*	*	*	*	*	*	*	*	*	1	1	1	0	0	0	0	0	0	1	1	1
		12	6	6	6	2	0	3	0	0	0	3	0	0	*	840	*	*	*	*	*	*	*	*	1	0	0	1	1	0	0	0	0	1	1	1
		12	6	12	0	2	0	0	3	0	0	0	3	0	*	*	840	*	*	*	*	*	*	*	0	1	0	1	0	1	0	0	0	1	0	2
		12	12	6	0	2	0	0	3	3	0	0	0	0	*	*	*	840	*	*	*	*	*	*	0	0	1	0	1	1	0	0	0	0	1	2
		12	6	0	12	0	3	3	0	0	0	0	0	2	*	*	*	*	840	*	*	*	*	*	1	0	0	0	0	0	1	1	0	1	2	0
		8	4	4	4	0	2	0	2	0	0	2	0	0	*	*	*	*	*	1260	*	*	*	*	0	1	0	0	1	0	1	0	0	1	1	1
		8	8	0	4	0	2	2	0	2	0	0	0	0	*	*	*	*	*	*	1260	*	*	*	0	0	1	0	1	0	0	1	0	0	2	1
		12	6	6	6	0	0	3	3	0	2	0	0	0	*	*	*	*	*	*	*	840	*	*	0	0	1	1	0	0	1	0	0	1	1	1
		24	0	12	24	0	0	0	0	0	4	6	0	4	*	*	*	*	*	*	*	*	420	*	1	0	0	0	0	0	1	0	1	2	1	0
		12	0	12	6	0	0	0	0	0	2	3	3	0	*	*	*	*	*	*	*	*	*	840	0	1	0	1	0	0	0	0	1	2	0	1
	f4	120	60	60	120	20	30	30	0	0	20	30	0	20	5	10	0	0	10	0	0	0	5	0	84	*	*	*	*	*	*	*	*	1	1	0
		48	24	48	24	8	12	0	12	0	8	12	12	0	2	0	4	0	0	6	0	0	0	4	*	210	*	*	*	*	*	*	*	1	0	1
		48	48	24	24	8	12	12	12	12	8	0	0	0	2	0	0	4	0	0	6	4	0	0	*	*	210	*	*	*	*	*	*	0	1	1
		36	18	36	18	6	0	9	9	0	6	9	9	0	0	3	3	0	0	0	0	3	0	3	*	*	*	280	*	*	*	*	*	1	0	1
		24	24	12	12	4	6	6	6	6	0	6	0	0	0	2	0	2	0	3	3	0	0	0	*	*	*	*	420	*	*	*	*	0	1	1
		36	36	36	0	12	0	0	18	9	0	0	9	0	0	0	6	6	0	0	0	0	0	0	*	*	*	*	*	140	*	*	*	0	0	2
		48	24	24	48	0	12	12	12	0	8	12	0	8	0	0	0	0	4	6	0	4	2	0	*	*	*	*	*	*	210	*	*	1	1	0
		24	24	0	24	0	12	12	0	6	0	0	0	4	0	0	0	0	4	0	6	0	0	0	*	*	*	*	*	*	*	210	*	0	2	0
		120	0	120	120	0	0	0	0	0	40	60	30	20	0	0	0	0	0	0	0	0	10	20	*	*	*	*	*	*	*	*	42	2	0	0
	f5	720	360	720	720	120	180	180	180	0	240	360	180	120	30	60	60	0	60	90	0	60	60	120	6	15	0	20	0	0	15	0	6	14	*	*
		240	240	120	240	40	120	120	60	60	40	60	0	40	10	20	0	20	40	30	60	20	10	0	2	0	5	0	10	0	5	10	0	*	42	*
		144	144	144	72	48	36	36	72	36	24	36	36	0	6	12	24	24	0	18	18	12	0	12	0	3	3	4	6	4	0	0	0	*	*	70

Full snub 6-simplex

The full snub 6-simplex or omnisnub 6-simplex, defined as an alternation of the omnitruncated 6-simplex is not uniform, but it can be given Coxeter diagram             and symmetry [[3,3,3,3,3]]⁺, and constructed from 14 snub 5-simplexes, 42 snub 5-cell antiprisms, 70 3-s{3,4} duoantiprisms, and 2520 irregular 5-simplexes filling the gaps at the deleted vertices.

Related uniform 6-polytopes

The pentellated 6-simplex is one of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A₆ Coxeter plane orthographic projections.

A6 polytopes
t0	t1	t2	t0,1	t0,2	t1,2	t0,3	t1,3	t2,3
t0,4	t1,4	t0,5	t0,1,2	t0,1,3	January 01, 1970 Latest articles January 07, 2023 No. 2705 Squadron RAF Regiment December 26, 2022 No. 299 Squadron RAF January 06, 2023 No. 208 Squadron RAF January 07, 2023 No. 213 Squadron RAF January 07, 2023 No. 231 Squadron RAF January 03, 2023 No. 237 Squadron RAF January 09, 2023 No. 2 Air Experience Flight RAF December 28, 2022 No. 341 Squadron RAF January 07, 2023 No. 37 Squadron IAF January 07, 2023 No. 39 Squadron RAF Most Read January 04, 2023 Skeletons Fighting over a Hanged Man January 03, 2023 Skeletons (Travis Scott song) January 06, 2023 Skelton Township, Warrick County, Indiana January 07, 2023 Skender Pasha January 06, 2023 Skerry's College pentellated, simplexes, simplex, pentellated, simplex, pentitruncated, simplex, penticantellated, simplex, penticantitruncated, simplex, pentiruncitruncated, simplex, pentiruncicantellated, simplex, pentiruncicantitruncated, simplex, pentisteritruncated, simpl. 6 simplex Pentellated 6 simplex Pentitruncated 6 simplex Penticantellated 6 simplex Penticantitruncated 6 simplex Pentiruncitruncated 6 simplex Pentiruncicantellated 6 simplex Pentiruncicantitruncated 6 simplex Pentisteritruncated 6 simplex Pentistericantitruncated 6 simplex Pentisteriruncicantitruncated 6 simplex Omnitruncated 6 simplex Orthogonal projections in A6 Coxeter plane In six dimensional geometry a pentellated 6 simplex is a convex uniform 6 polytope with 5th order truncations of the regular 6 simplex There are unique 10 degrees of pentellations of the 6 simplex with permutations of truncations cantellations runcinations and sterications The simple pentellated 6 simplex is also called an expanded 6 simplex constructed by an expansion operation applied to the regular 6 simplex The highest form the pentisteriruncicantitruncated 6 simplex is called an omnitruncated 6 simplex with all of the nodes ringed Contents 1 Pentellated 6 simplex 1 1 Alternate names 1 2 Cross sections 1 3 Coordinates 1 4 Root vectors 1 5 Images 1 6 Configuration 2 Pentitruncated 6 simplex 2 1 Alternate names 2 2 Coordinates 2 3 Images 3 Penticantellated 6 simplex 3 1 Alternate names 3 2 Coordinates 3 3 Images 4 Penticantitruncated 6 simplex 4 1 Alternate names 4 2 Coordinates 4 3 Images 5 Pentiruncitruncated 6 simplex 5 1 Alternate names 5 2 Coordinates 5 3 Images 6 Pentiruncicantellated 6 simplex 6 1 Alternate names 6 2 Coordinates 6 3 Images 7 Pentiruncicantitruncated 6 simplex 7 1 Alternate names 7 2 Coordinates 7 3 Images 8 Pentisteritruncated 6 simplex 8 1 Alternate names 8 2 Coordinates 8 3 Images 9 Pentistericantitruncated 6 simplex 9 1 Alternate names 9 2 Coordinates 9 3 Images 10 Omnitruncated 6 simplex 10 1 Alternate names 10 2 Permutohedron and related tessellation 10 3 Coordinates 10 4 Images 10 5 Configuration 10 6 Full snub 6 simplex 11 Related uniform 6 polytopes 12 Notes 13 References 14 External linksPentellated 6 simplex editPentellated 6 simplex Type Uniform 6 polytope Schlafli symbol t0 5 3 3 3 3 3 Coxeter Dynkin diagram nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 7 7 34 nbsp 21 21 3 3 3 35 35 3 3 3 4 faces 434 Cells 630 Faces 490 Edges 210 Vertices 42 Vertex figure 5 cell antiprism Coxeter group A6 2 3 3 3 3 3 order 10080 Properties convex Alternate names edit Expanded 6 simplex Small terated tetradecapeton Acronym staf Jonathan Bowers 1 Cross sections edit The maximal cross section of the pentellated 6 simplex with a 5 dimensional hyperplane is a stericated hexateron This cross section divides the pentellated 6 simplex into two hexateral hypercupolas consisting of 7 5 simplexes 21 5 cell prisms and 35 Tetrahedral Triangular duoprisms each Coordinates edit The vertices of the pentellated 6 simplex can be positioned in 7 space as permutations of 0 1 1 1 1 1 2 This construction is based on facets of the pentellated 7 orthoplex A second construction in 7 space from the center of a rectified 7 orthoplex is given by coordinate permutations of 1 1 0 0 0 0 0 Root vectors edit Its 42 vertices represent the root vectors of the simple Lie group A6 It is the vertex figure of the 6 simplex honeycomb Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Symmetry 7 14 6 5 10 Ak Coxeter plane A3 A2 Graph nbsp nbsp Symmetry 4 3 6 Note Symmetry doubled for Ak graphs with even k due to symmetrically ringed Coxeter Dynkin diagram Configuration edit This configuration matrix represents the expanded 6 simplex with 12 permutations of elements The rows and columns correspond to vertices edges faces cells 4 faces and 5 faces The diagonal numbers say how many of each element occur in the whole polytope The nondiagonal numbers say how many of the column s element occur in or at the row s element 2 Element fk f0 f1 f2 f3 f4 f5 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f0 42 10 20 20 20 60 10 40 30 2 10 20 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f1 2 210 4 4 6 18 4 16 12 1 5 10 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f2 3 3 280 3 3 3 6 3 1 3 4 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 4 210 0 6 0 6 6 0 2 6 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f3 4 6 4 0 210 2 2 0 1 2 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 9 2 3 420 0 2 2 0 1 3 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f4 5 10 10 0 5 0 84 1 1 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 8 16 8 6 2 4 210 0 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 9 18 6 9 0 6 140 0 0 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f5 6 15 20 0 15 0 6 0 0 14 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 10 25 20 10 10 10 2 5 0 42 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 12 30 16 18 3 18 0 3 4 70Pentitruncated 6 simplex editPentitruncated 6 simplex Type uniform 6 polytope Schlafli symbol t0 1 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 826 Cells 1785 Faces 1820 Edges 945 Vertices 210 Vertex figure Coxeter group A6 3 3 3 3 3 order 5040 Properties convex Alternate names edit Teracellated heptapeton Acronym tocal Jonathan Bowers 3 Coordinates edit The vertices of the runcitruncated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 1 1 1 2 3 This construction is based on facets of the runcitruncated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Dihedral symmetry 7 6 5 Ak Coxeter plane A3 A2 Graph nbsp nbsp Dihedral symmetry 4 3 Penticantellated 6 simplex editPenticantellated 6 simplex Type uniform 6 polytope Schlafli symbol t0 2 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 1246 Cells 3570 Faces 4340 Edges 2310 Vertices 420 Vertex figure Coxeter group A6 3 3 3 3 3 order 5040 Properties convex Alternate names edit Teriprismated heptapeton Acronym topal Jonathan Bowers 4 Coordinates edit The vertices of the runcicantellated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 1 1 1 2 3 This construction is based on facets of the penticantellated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Dihedral symmetry 7 6 5 Ak Coxeter plane A3 A2 Graph nbsp nbsp Dihedral symmetry 4 3 Penticantitruncated 6 simplex editpenticantitruncated 6 simplex Type uniform 6 polytope Schlafli symbol t0 1 2 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 1351 Cells 4095 Faces 5390 Edges 3360 Vertices 840 Vertex figure Coxeter group A6 3 3 3 3 3 order 5040 Properties convex Alternate names edit Terigreatorhombated heptapeton Acronym togral Jonathan Bowers 5 Coordinates edit The vertices of the penticantitruncated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 1 1 2 3 4 This construction is based on facets of the penticantitruncated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Dihedral symmetry 7 6 5 Ak Coxeter plane A3 A2 Graph nbsp nbsp Dihedral symmetry 4 3 Pentiruncitruncated 6 simplex editpentiruncitruncated 6 simplex Type uniform 6 polytope Schlafli symbol t0 1 3 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 1491 Cells 5565 Faces 8610 Edges 5670 Vertices 1260 Vertex figure Coxeter group A6 3 3 3 3 3 order 5040 Properties convex Alternate names edit Tericellirhombated heptapeton Acronym tocral Jonathan Bowers 6 Coordinates edit The vertices of the pentiruncitruncated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 1 1 2 3 4 This construction is based on facets of the pentiruncitruncated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Dihedral symmetry 7 6 5 Ak Coxeter plane A3 A2 Graph nbsp nbsp Dihedral symmetry 4 3 Pentiruncicantellated 6 simplex editPentiruncicantellated 6 simplex Type uniform 6 polytope Schlafli symbol t0 2 3 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 1596 Cells 5250 Faces 7560 Edges 5040 Vertices 1260 Vertex figure Coxeter group A6 3 3 3 3 3 order 10080 Properties convex Alternate names edit Teriprismatorhombated tetradecapeton Acronym taporf Jonathan Bowers 7 Coordinates edit The vertices of the pentiruncicantellated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 1 2 3 3 4 This construction is based on facets of the pentiruncicantellated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Symmetry 7 14 6 5 10 Ak Coxeter plane A3 A2 Graph nbsp nbsp Symmetry 4 3 6 Note Symmetry doubled for Ak graphs with even k due to symmetrically ringed Coxeter Dynkin diagram Pentiruncicantitruncated 6 simplex editPentiruncicantitruncated 6 simplex Type uniform 6 polytope Schlafli symbol t0 1 2 3 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 1701 Cells 6825 Faces 11550 Edges 8820 Vertices 2520 Vertex figure Coxeter group A6 3 3 3 3 3 order 5040 Properties convex Alternate names edit Terigreatoprismated heptapeton Acronym tagopal Jonathan Bowers 8 Coordinates edit The vertices of the pentiruncicantitruncated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 1 2 3 4 5 This construction is based on facets of the pentiruncicantitruncated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Dihedral symmetry 7 6 5 Ak Coxeter plane A3 A2 Graph nbsp nbsp Dihedral symmetry 4 3 Pentisteritruncated 6 simplex editPentisteritruncated 6 simplex Type uniform 6 polytope Schlafli symbol t0 1 4 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 1176 Cells 3780 Faces 5250 Edges 3360 Vertices 840 Vertex figure Coxeter group A6 3 3 3 3 3 order 10080 Properties convex Alternate names edit Tericellitruncated tetradecapeton Acronym tactaf Jonathan Bowers 9 Coordinates edit The vertices of the pentisteritruncated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 2 2 2 3 4 This construction is based on facets of the pentisteritruncated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Symmetry 7 14 6 5 10 Ak Coxeter plane A3 A2 Graph nbsp nbsp Symmetry 4 3 6 Note Symmetry doubled for Ak graphs with even k due to symmetrically ringed Coxeter Dynkin diagram Pentistericantitruncated 6 simplex editpentistericantitruncated 6 simplex Type uniform 6 polytope Schlafli symbol t0 1 2 4 5 3 3 3 3 3 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 4 faces 1596 Cells 6510 Faces 11340 Edges 8820 Vertices 2520 Vertex figure Coxeter group A6 3 3 3 3 3 order 5040 Properties convex Alternate names edit Great teracellirhombated heptapeton Acronym gatocral Jonathan Bowers 10 Coordinates edit The vertices of the pentistericantittruncated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 2 2 3 4 5 This construction is based on facets of the pentistericantitruncated 7 orthoplex Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Dihedral symmetry 7 6 5 Ak Coxeter plane A3 A2 Graph nbsp nbsp Dihedral symmetry 4 3 Omnitruncated 6 simplex editOmnitruncated 6 simplex Type Uniform 6 polytope Schlafli symbol t0 1 2 3 4 5 35 Coxeter Dynkin diagrams nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 5 faces 126 14 t0 1 2 3 4 34 nbsp 42 t0 1 2 3 33 nbsp nbsp 70 6 t0 1 2 3 3 nbsp nbsp 4 faces 1806 Cells 8400 Faces 16800 4200 6 nbsp 1260 4 nbsp Edges 15120 Vertices 5040 Vertex figure nbsp irregular 5 simplex Coxeter group A6 35 order 10080 Properties convex isogonal zonotope The omnitruncated 6 simplex has 5040 vertices 15120 edges 16800 faces 4200 hexagons and 1260 squares 8400 cells 1806 4 faces and 126 5 faces With 5040 vertices it is the largest of 35 uniform 6 polytopes generated from the regular 6 simplex Alternate names edit Pentisteriruncicantitruncated 6 simplex Johnson s omnitruncation for 6 polytopes Omnitruncated heptapeton Great terated tetradecapeton Acronym gotaf Jonathan Bowers 11 Permutohedron and related tessellation edit The omnitruncated 6 simplex is the permutohedron of order 7 The omnitruncated 6 simplex is a zonotope the Minkowski sum of seven line segments parallel to the seven lines through the origin and the seven vertices of the 6 simplex Like all uniform omnitruncated n simplices the omnitruncated 6 simplex can tessellate space by itself in this case 6 dimensional space with three facets around each hypercell It has Coxeter Dynkin diagram of nbsp nbsp nbsp nbsp nbsp nbsp nbsp Coordinates edit The vertices of the omnitruncated 6 simplex can be most simply positioned in 7 space as permutations of 0 1 2 3 4 5 6 This construction is based on facets of the pentisteriruncicantitruncated 7 orthoplex t0 1 2 3 4 5 35 4 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp Images edit orthographic projections Ak Coxeter plane A6 A5 A4 Graph nbsp nbsp nbsp Symmetry 7 14 6 5 10 Ak Coxeter plane A3 A2 Graph nbsp nbsp Symmetry 4 3 6 Note Symmetry doubled for Ak graphs with even k due to symmetrically ringed Coxeter Dynkin diagram Configuration edit This configuration matrix represents the omnitruncated 6 simplex with 35 permutations of elements The rows and columns correspond to vertices edges faces cells 4 faces and 5 faces The diagonal numbers say how many of each element occur in the whole polytope The nondiagonal numbers say how many of the column s element occur in or at the row s element 12 Element fk f0 f1 f2 f3 f4 f5 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f0 5040 2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f1 2 5040 1 1 1 1 1 0 0 0 0 1 1 1 2 1 1 2 1 0 0 1 1 2 1 2 1 1 1 0 1 2 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 2 5040 1 0 0 1 0 1 1 1 0 1 1 2 1 0 1 0 1 1 2 1 2 1 2 1 1 1 0 1 2 1 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 2 5040 0 1 1 0 0 1 1 0 1 1 1 0 0 2 1 1 1 2 1 2 1 1 1 1 0 2 1 1 2 2 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f2 6 3 3 0 1680 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 2 0 2 2520 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 2 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 2 0 2 2520 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 2 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 2 2 0 2520 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 4 0 0 1260 0 0 0 2 0 0 2 0 0 0 0 0 2 0 2 1 0 1 0 0 2 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 0 3 3 1680 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 2 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 0 2 2 2520 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 2 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 4 0 4 0 1260 0 0 2 0 0 0 0 0 0 2 0 2 0 2 0 1 0 0 1 2 0 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 6 0 0 6 840 0 0 0 0 2 0 0 0 2 0 2 0 0 0 0 0 2 1 1 2 2 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f3 24 12 12 12 4 6 0 0 0 4 0 0 0 420 1 1 1 0 0 0 0 0 0 1 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 12 6 6 6 2 0 3 0 0 0 3 0 0 840 1 0 0 1 1 0 0 0 0 1 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 12 6 12 0 2 0 0 3 0 0 0 3 0 840 0 1 0 1 0 1 0 0 0 1 0 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 12 12 6 0 2 0 0 3 3 0 0 0 0 840 0 0 1 0 1 1 0 0 0 0 1 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 12 6 0 12 0 3 3 0 0 0 0 0 2 840 1 0 0 0 0 0 1 1 0 1 2 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 8 4 4 4 0 2 0 2 0 0 2 0 0 1260 0 1 0 0 1 0 1 0 0 1 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 8 8 0 4 0 2 2 0 2 0 0 0 0 1260 0 0 1 0 1 0 0 1 0 0 2 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 12 6 6 6 0 0 3 3 0 2 0 0 0 840 0 0 1 1 0 0 1 0 0 1 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 24 0 12 24 0 0 0 0 0 4 6 0 4 420 1 0 0 0 0 0 1 0 1 2 1 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 12 0 12 6 0 0 0 0 0 2 3 3 0 840 0 1 0 1 0 0 0 0 1 2 0 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f4 120 60 60 120 20 30 30 0 0 20 30 0 20 5 10 0 0 10 0 0 0 5 0 84 1 1 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 48 24 48 24 8 12 0 12 0 8 12 12 0 2 0 4 0 0 6 0 0 0 4 210 1 0 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 48 48 24 24 8 12 12 12 12 8 0 0 0 2 0 0 4 0 0 6 4 0 0 210 0 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 36 18 36 18 6 0 9 9 0 6 9 9 0 0 3 3 0 0 0 0 3 0 3 280 1 0 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 24 24 12 12 4 6 6 6 6 0 6 0 0 0 2 0 2 0 3 3 0 0 0 420 0 1 1 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 36 36 36 0 12 0 0 18 9 0 0 9 0 0 0 6 6 0 0 0 0 0 0 140 0 0 2 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 48 24 24 48 0 12 12 12 0 8 12 0 8 0 0 0 0 4 6 0 4 2 0 210 1 1 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 24 24 0 24 0 12 12 0 6 0 0 0 4 0 0 0 0 4 0 6 0 0 0 210 0 2 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 120 0 120 120 0 0 0 0 0 40 60 30 20 0 0 0 0 0 0 0 0 10 20 42 2 0 0 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp f5 720 360 720 720 120 180 180 180 0 240 360 180 120 30 60 60 0 60 90 0 60 60 120 6 15 0 20 0 0 15 0 6 14 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 240 240 120 240 40 120 120 60 60 40 60 0 40 10 20 0 20 40 30 60 20 10 0 2 0 5 0 10 0 5 10 0 42 nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 144 144 144 72 48 36 36 72 36 24 36 36 0 6 12 24 24 0 18 18 12 0 12 0 3 3 4 6 4 0 0 0 70 Full snub 6 simplex edit The full snub 6 simplex or omnisnub 6 simplex defined as an alternation of the omnitruncated 6 simplex is not uniform but it can be given Coxeter diagram nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp and symmetry 3 3 3 3 3 and constructed from 14 snub 5 simplexes 42 snub 5 cell antiprisms 70 3 s 3 4 duoantiprisms and 2520 irregular 5 simplexes filling the gaps at the deleted vertices Related uniform 6 polytopes editThe pentellated 6 simplex is one of 35 uniform 6 polytopes based on the 3 3 3 3 3 Coxeter group all shown here in A6 Coxeter plane orthographic projections A6 polytopes nbsp t0 nbsp t1 nbsp t2 nbsp t0 1 nbsp t0 2 nbsp t1 2 nbsp t0 3 nbsp t1 3 nbsp t2 3 nbsp t0 4 nbsp t1 4 nbsp t0 5 nbsp t0 1 2 nbsp t0 1 3 nbsp a tit, wikipedia, wiki, book, books, library, article , read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games. © Copyright 2021, All Rights Reserved  |   www.wiki3.en-us.nina.az Rss Feed SiteMap Ping DMCA Contact Us HomePage Closed Call: