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A7 polytope

[[File:7-simplex t0.svg	160px]]7-simplex

In 7-dimensional geometry, there are 71 uniform polytopes with A7 symmetry. There is one self-dual regular form, the 7-simplex with 8 vertices.

Each can be visualized as symmetric orthographic projections in Coxeter planes of the A7 Coxeter group, and other subgroups.

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Graphs

Symmetric orthographic projections of these 71 polytopes can be made in the A7, A6, A5, A4, A3, A2 Coxeter planes. Ak has [k+1] symmetry. For even k and symmetrically ringed-diagrams, symmetry doubles to [2(k+1)].

These 71 polytopes are each shown in these 6 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

#	Coxeter-Dynkin diagram
Schläfli symbol
Johnson name	Ak orthogonal projection graphs	A7[8]	A6[7]	A5[6]	A4[5]	A3[4]	A2[3]	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71

t0{3,3,3,3,3,3}
7-simplex	[[File:7-simplex t0.svg	80px]]	[[File:7-simplex t0 A6.svg	80px]]	[[File:7-simplex t0 A5.svg	80px]]	[[File:7-simplex t0 A4.svg	80px]]	[[File:7-simplex t0 A3.svg	80px]]	[[File:7-simplex t0 A2.svg	80px]]

t1{3,3,3,3,3,3}
Rectified 7-simplex	[[File:7-simplex t1.svg	80px]]	[[File:7-simplex t1 A6.svg	80px]]	[[File:7-simplex t1 A5.svg	80px]]	[[File:7-simplex t1 A4.svg	80px]]	[[File:7-simplex t1 A3.svg	80px]]	[[File:7-simplex t1 A2.svg	80px]]

t2{3,3,3,3,3,3}
Birectified 7-simplex	[[File:7-simplex t2.svg	80px]]	[[File:7-simplex t2 A6.svg	80px]]	[[File:7-simplex t2 A5.svg	80px]]	[[File:7-simplex t2 A4.svg	80px]]	[[File:7-simplex t2 A3.svg	80px]]	[[File:7-simplex t2 A2.svg	80px]]

t3{3,3,3,3,3,3}
Trirectified 7-simplex	[[File:7-simplex t3.svg	80px]]	[[File:7-simplex t3 A6.svg	80px]]	[[File:7-simplex t3 A5.svg	80px]]	[[File:7-simplex t3 A4.svg	80px]]	[[File:7-simplex t3 A3.svg	80px]]	[[File:7-simplex t3 A2.svg	80px]]

t0,1{3,3,3,3,3,3}
Truncated 7-simplex	[[File:7-simplex t01.svg	80px]]	[[File:7-simplex t01 A6.svg	80px]]	[[File:7-simplex t01 A5.svg	80px]]	[[File:7-simplex t01 A4.svg	80px]]	[[File:7-simplex t01 A3.svg	80px]]	[[File:7-simplex t01 A2.svg	80px]]

t0,2{3,3,3,3,3,3}
Cantellated 7-simplex	[[File:7-simplex t02.svg	80px]]	[[File:7-simplex t02 A6.svg	80px]]	[[File:7-simplex t02 A5.svg	80px]]	[[File:7-simplex t02 A4.svg	80px]]	[[File:7-simplex t02 A3.svg	80px]]	[[File:7-simplex t02 A2.svg	80px]]

t1,2{3,3,3,3,3,3}
Bitruncated 7-simplex	[[File:7-simplex t12.svg	80px]]	[[File:7-simplex t12 A6.svg	80px]]	[[File:7-simplex t12 A5.svg	80px]]	[[File:7-simplex t12 A4.svg	80px]]	[[File:7-simplex t12 A3.svg	80px]]	[[File:7-simplex t12 A2.svg	80px]]

t0,3{3,3,3,3,3,3}
Runcinated 7-simplex	[[File:7-simplex t03.svg	80px]]	[[File:7-simplex t03 A6.svg	80px]]	[[File:7-simplex t03 A5.svg	80px]]	[[File:7-simplex t03 A4.svg	80px]]	[[File:7-simplex t03 A3.svg	80px]]	[[File:7-simplex t03 A2.svg	80px]]

t1,3{3,3,3,3,3,3}
Bicantellated 7-simplex	[[File:7-simplex t13.svg	80px]]	[[File:7-simplex t13 A6.svg	80px]]	[[File:7-simplex t13 A5.svg	80px]]	[[File:7-simplex t13 A4.svg	80px]]	[[File:7-simplex t13 A3.svg	80px]]	[[File:7-simplex t13 A2.svg	80px]]

t2,3{3,3,3,3,3,3}
Tritruncated 7-simplex	[[File:7-simplex t23.svg	80px]]	[[File:7-simplex t23 A6.svg	80px]]	[[File:7-simplex t23 A5.svg	80px]]	[[File:7-simplex t23 A4.svg	80px]]	[[File:7-simplex t23 A3.svg	80px]]	[[File:7-simplex t23 A2.svg	80px]]

t0,4{3,3,3,3,3,3}
Stericated 7-simplex	[[File:7-simplex t04.svg	80px]]	[[File:7-simplex t04 A6.svg	80px]]	[[File:7-simplex t04 A5.svg	80px]]	[[File:7-simplex t04 A4.svg	80px]]	[[File:7-simplex t04 A3.svg	80px]]	[[File:7-simplex t04 A2.svg	80px]]

t1,4{3,3,3,3,3,3}
Biruncinated 7-simplex	[[File:7-simplex t14.svg	80px]]	[[File:7-simplex t14 A6.svg	80px]]	[[File:7-simplex t14 A5.svg	80px]]	[[File:7-simplex t14 A4.svg	80px]]	[[File:7-simplex t14 A3.svg	80px]]	[[File:7-simplex t14 A2.svg	80px]]

t2,4{3,3,3,3,3,3}
Tricantellated 7-simplex	[[File:7-simplex t24.svg	80px]]	[[File:7-simplex t24 A6.svg	80px]]	[[File:7-simplex t24 A5.svg	80px]]	[[File:7-simplex t24 A4.svg	80px]]	[[File:7-simplex t24 A3.svg	80px]]	[[File:7-simplex t24 A2.svg	80px]]

t0,5{3,3,3,3,3,3}
Pentellated 7-simplex	[[File:7-simplex t05.svg	80px]]	[[File:7-simplex t05 A6.svg	80px]]	[[File:7-simplex t05 A5.svg	80px]]	[[File:7-simplex t05 A4.svg	80px]]	[[File:7-simplex t05 A3.svg	80px]]	[[File:7-simplex t05 A2.svg	80px]]

t1,5{3,3,3,3,3,3}
Bistericated 7-simplex	[[File:7-simplex t15.svg	80px]]	[[File:7-simplex t15 A6.svg	80px]]	[[File:7-simplex t15 A5.svg	80px]]	[[File:7-simplex t15 A4.svg	80px]]	[[File:7-simplex t15 A3.svg	80px]]	[[File:7-simplex t15 A2.svg	80px]]

t0,6{3,3,3,3,3,3}
Hexicated 7-simplex	[[File:7-simplex t06.svg	80px]]	[[File:7-simplex t06 A6.svg	80px]]	[[File:7-simplex t06 A5.svg	80px]]	[[File:7-simplex t06 A4.svg	80px]]	[[File:7-simplex t06 A3.svg	80px]]	[[File:7-simplex t06 A2.svg	80px]]

t0,1,2{3,3,3,3,3,3}
Cantitruncated 7-simplex	[[File:7-simplex t012.svg	80px]]	[[File:7-simplex t012 A6.svg	80px]]	[[File:7-simplex t012 A5.svg	80px]]	[[File:7-simplex t012 A4.svg	80px]]	[[File:7-simplex t012 A3.svg	80px]]	[[File:7-simplex t012 A2.svg	80px]]

t0,1,3{3,3,3,3,3,3}
Runcitruncated 7-simplex	[[File:7-simplex t013.svg	80px]]	[[File:7-simplex t013 A6.svg	80px]]	[[File:7-simplex t013 A5.svg	80px]]	[[File:7-simplex t013 A4.svg	80px]]	[[File:7-simplex t013 A3.svg	80px]]	[[File:7-simplex t013 A2.svg	80px]]

t0,2,3{3,3,3,3,3,3}
Runcicantellated 7-simplex	[[File:7-simplex t023.svg	80px]]	[[File:7-simplex t023 A6.svg	80px]]	[[File:7-simplex t023 A5.svg	80px]]	[[File:7-simplex t023 A4.svg	80px]]	[[File:7-simplex t023 A3.svg	80px]]	[[File:7-simplex t023 A2.svg	80px]]

t1,2,3{3,3,3,3,3,3}
Bicantitruncated 7-simplex	[[File:7-simplex t123.svg	80px]]	[[File:7-simplex t123 A6.svg	80px]]	[[File:7-simplex t123 A5.svg	80px]]	[[File:7-simplex t123 A4.svg	80px]]	[[File:7-simplex t123 A3.svg	80px]]	[[File:7-simplex t123 A2.svg	80px]]

t0,1,4{3,3,3,3,3,3}
Steritruncated 7-simplex	[[File:7-simplex t014.svg	80px]]	[[File:7-simplex t014 A6.svg	80px]]	[[File:7-simplex t014 A5.svg	80px]]	[[File:7-simplex t014 A4.svg	80px]]	[[File:7-simplex t014 A3.svg	80px]]	[[File:7-simplex t014 A2.svg	80px]]

t0,2,4{3,3,3,3,3,3}
Stericantellated 7-simplex	[[File:7-simplex t024.svg	80px]]	[[File:7-simplex t024 A6.svg	80px]]	[[File:7-simplex t024 A5.svg	80px]]	[[File:7-simplex t024 A4.svg	80px]]	[[File:7-simplex t024 A3.svg	80px]]	[[File:7-simplex t024 A2.svg	80px]]

t1,2,4{3,3,3,3,3,3}
Biruncitruncated 7-simplex	[[File:7-simplex t124.svg	80px]]	[[File:7-simplex t124 A6.svg	80px]]	[[File:7-simplex t124 A5.svg	80px]]	[[File:7-simplex t124 A4.svg	80px]]	[[File:7-simplex t124 A3.svg	80px]]	[[File:7-simplex t124 A2.svg	80px]]

t0,3,4{3,3,3,3,3,3}
Steriruncinated 7-simplex	[[File:7-simplex t034.svg	80px]]	[[File:7-simplex t034 A6.svg	80px]]	[[File:7-simplex t034 A5.svg	80px]]	[[File:7-simplex t034 A4.svg	80px]]	[[File:7-simplex t034 A3.svg	80px]]	[[File:7-simplex t034 A2.svg	80px]]

t1,3,4{3,3,3,3,3,3}
Biruncicantellated 7-simplex	[[File:7-simplex t134.svg	80px]]	[[File:7-simplex t134 A6.svg	80px]]	[[File:7-simplex t134 A5.svg	80px]]	[[File:7-simplex t134 A4.svg	80px]]	[[File:7-simplex t134 A3.svg	80px]]	[[File:7-simplex t134 A2.svg	80px]]

t2,3,4{3,3,3,3,3,3}
Tricantitruncated 7-simplex	[[File:7-simplex t234.svg	80px]]	[[File:7-simplex t234 A6.svg	80px]]	[[File:7-simplex t234 A5.svg	80px]]	[[File:7-simplex t234 A4.svg	80px]]	[[File:7-simplex t234 A3.svg	80px]]	[[File:7-simplex t234 A2.svg	80px]]

t0,1,5{3,3,3,3,3,3}
Pentitruncated 7-simplex	[[File:7-simplex t015.svg	80px]]	[[File:7-simplex t015 A6.svg	80px]]	[[File:7-simplex t015 A5.svg	80px]]	[[File:7-simplex t015 A4.svg	80px]]	[[File:7-simplex t015 A3.svg	80px]]	[[File:7-simplex t015 A2.svg	80px]]

t0,2,5{3,3,3,3,3,3}
Penticantellated 7-simplex	[[File:7-simplex t025.svg	80px]]	[[File:7-simplex t025 A6.svg	80px]]	[[File:7-simplex t025 A5.svg	80px]]	[[File:7-simplex t025 A4.svg	80px]]	[[File:7-simplex t025 A3.svg	80px]]	[[File:7-simplex t025 A2.svg	80px]]

t1,2,5{3,3,3,3,3,3}
Bisteritruncated 7-simplex	[[File:7-simplex t125.svg	80px]]	[[File:7-simplex t125 A6.svg	80px]]	[[File:7-simplex t125 A5.svg	80px]]	[[File:7-simplex t125 A4.svg	80px]]	[[File:7-simplex t125 A3.svg	80px]]	[[File:7-simplex t125 A2.svg	80px]]

t0,3,5{3,3,3,3,3,3}
Pentiruncinated 7-simplex	[[File:7-simplex t035.svg	80px]]	[[File:7-simplex t035 A6.svg	80px]]	[[File:7-simplex t035 A5.svg	80px]]	[[File:7-simplex t035 A4.svg	80px]]	[[File:7-simplex t035 A3.svg	80px]]	[[File:7-simplex t035 A2.svg	80px]]

t1,3,5{3,3,3,3,3,3}
Bistericantellated 7-simplex	[[File:7-simplex t135.svg	80px]]	[[File:7-simplex t135 A6.svg	80px]]	[[File:7-simplex t135 A5.svg	80px]]	[[File:7-simplex t135 A4.svg	80px]]	[[File:7-simplex t135 A3.svg	80px]]	[[File:7-simplex t135 A2.svg	80px]]

t0,4,5{3,3,3,3,3,3}
Pentistericated 7-simplex	[[File:7-simplex t045.svg	80px]]	[[File:7-simplex t045 A6.svg	80px]]	[[File:7-simplex t045 A5.svg	80px]]	[[File:7-simplex t045 A4.svg	80px]]	[[File:7-simplex t045 A3.svg	80px]]	[[File:7-simplex t045 A2.svg	80px]]

t0,1,6{3,3,3,3,3,3}
Hexitruncated 7-simplex	[[File:7-simplex t016.svg	80px]]	[[File:7-simplex t016 A6.svg	80px]]	[[File:7-simplex t016 A5.svg	80px]]	[[File:7-simplex t016 A4.svg	80px]]	[[File:7-simplex t016 A3.svg	80px]]	[[File:7-simplex t016 A2.svg	80px]]

t0,2,6{3,3,3,3,3,3}
Hexicantellated 7-simplex	[[File:7-simplex t026.svg	80px]]	[[File:7-simplex t026 A6.svg	80px]]	[[File:7-simplex t026 A5.svg	80px]]	[[File:7-simplex t026 A4.svg	80px]]	[[File:7-simplex t026 A3.svg	80px]]	[[File:7-simplex t026 A2.svg	80px]]

t0,3,6{3,3,3,3,3,3}
Hexiruncinated 7-simplex	[[File:7-simplex t036.svg	80px]]	[[File:7-simplex t036 A6.svg	80px]]	[[File:7-simplex t036 A5.svg	80px]]	[[File:7-simplex t036 A4.svg	80px]]	[[File:7-simplex t036 A3.svg	80px]]	[[File:7-simplex t036 A2.svg	80px]]

t0,1,2,3{3,3,3,3,3,3}
Runcicantitruncated 7-simplex	[[File:7-simplex t0123.svg	80px]]	[[File:7-simplex t0123 A6.svg	80px]]	[[File:7-simplex t0123 A5.svg	80px]]	[[File:7-simplex t0123 A4.svg	80px]]	[[File:7-simplex t0123 A3.svg	80px]]	[[File:7-simplex t0123 A2.svg	80px]]

t0,1,2,4{3,3,3,3,3,3}
Stericantitruncated 7-simplex	[[File:7-simplex t0124.svg	80px]]	[[File:7-simplex t0124 A6.svg	80px]]	[[File:7-simplex t0124 A5.svg	80px]]	[[File:7-simplex t0124 A4.svg	80px]]	[[File:7-simplex t0124 A3.svg	80px]]	[[File:7-simplex t0124 A2.svg	80px]]

t0,1,3,4{3,3,3,3,3,3}
Steriruncitruncated 7-simplex	[[File:7-simplex t0134.svg	80px]]	[[File:7-simplex t0134 A6.svg	80px]]	[[File:7-simplex t0134 A5.svg	80px]]	[[File:7-simplex t0134 A4.svg	80px]]	[[File:7-simplex t0134 A3.svg	80px]]	[[File:7-simplex t0134 A2.svg	80px]]

t0,2,3,4{3,3,3,3,3,3}
Steriruncicantellated 7-simplex	[[File:7-simplex t0234.svg	80px]]	[[File:7-simplex t0234 A6.svg	80px]]	[[File:7-simplex t0234 A5.svg	80px]]	[[File:7-simplex t0234 A4.svg	80px]]	[[File:7-simplex t0234 A3.svg	80px]]	[[File:7-simplex t0234 A2.svg	80px]]

t1,2,3,4{3,3,3,3,3,3}
Biruncicantitruncated 7-simplex	[[File:7-simplex t1234.svg	80px]]	[[File:7-simplex t1234 A6.svg	80px]]	[[File:7-simplex t1234 A5.svg	80px]]	[[File:7-simplex t1234 A4.svg	80px]]	[[File:7-simplex t1234 A3.svg	80px]]	[[File:7-simplex t1234 A2.svg	80px]]

t0,1,2,5{3,3,3,3,3,3}
Penticantitruncated 7-simplex	[[File:7-simplex t0125.svg	80px]]	[[File:7-simplex t0125 A6.svg	80px]]	[[File:7-simplex t0125 A5.svg	80px]]	[[File:7-simplex t0125 A4.svg	80px]]	[[File:7-simplex t0125 A3.svg	80px]]	[[File:7-simplex t0125 A2.svg	80px]]

t0,1,3,5{3,3,3,3,3,3}
Pentiruncitruncated 7-simplex	[[File:7-simplex t0135.svg	80px]]	[[File:7-simplex t0135 A6.svg	80px]]	[[File:7-simplex t0135 A5.svg	80px]]	[[File:7-simplex t0135 A4.svg	80px]]	[[File:7-simplex t0135 A3.svg	80px]]	[[File:7-simplex t0135 A2.svg	80px]]

t0,2,3,5{3,3,3,3,3,3}
Pentiruncicantellated 7-simplex	[[File:7-simplex t0235.svg	80px]]	[[File:7-simplex t0235 A6.svg	80px]]	[[File:7-simplex t0235 A5.svg	80px]]	[[File:7-simplex t0235 A4.svg	80px]]	[[File:7-simplex t0235 A3.svg	80px]]	[[File:7-simplex t0235 A2.svg	80px]]

t1,2,3,5{3,3,3,3,3,3}
Bistericantitruncated 7-simplex	[[File:7-simplex t1235.svg	80px]]	[[File:7-simplex t1235 A6.svg	80px]]	[[File:7-simplex t1235 A5.svg	80px]]	[[File:7-simplex t1235 A4.svg	80px]]	[[File:7-simplex t1235 A3.svg	80px]]	[[File:7-simplex t1235 A2.svg	80px]]

t0,1,4,5{3,3,3,3,3,3}
Pentisteritruncated 7-simplex	[[File:7-simplex t0145.svg	80px]]	[[File:7-simplex t0145 A6.svg	80px]]	[[File:7-simplex t0145 A5.svg	80px]]	[[File:7-simplex t0145 A4.svg	80px]]	[[File:7-simplex t0145 A3.svg	80px]]	[[File:7-simplex t0145 A2.svg	80px]]

t0,2,4,5{3,3,3,3,3,3}
Pentistericantellated 7-simplex	[[File:7-simplex t0245.svg	80px]]	[[File:7-simplex t0245 A6.svg	80px]]	[[File:7-simplex t0245 A5.svg	80px]]	[[File:7-simplex t0245 A4.svg	80px]]	[[File:7-simplex t0245 A3.svg	80px]]	[[File:7-simplex t0245 A2.svg	80px]]

t1,2,4,5{3,3,3,3,3,3}
Bisteriruncitruncated 7-simplex	[[File:7-simplex t1245.svg	80px]]	[[File:7-simplex t1245 A6.svg	80px]]	[[File:7-simplex t1245 A5.svg	80px]]	[[File:7-simplex t1245 A4.svg	80px]]	[[File:7-simplex t1245 A3.svg	80px]]	[[File:7-simplex t1245 A2.svg	80px]]

t0,3,4,5{3,3,3,3,3,3}
Pentisteriruncinated 7-simplex	[[File:7-simplex t0345.svg	80px]]	[[File:7-simplex t0345 A6.svg	80px]]	[[File:7-simplex t0345 A5.svg	80px]]	[[File:7-simplex t0345 A4.svg	80px]]	[[File:7-simplex t0345 A3.svg	80px]]	[[File:7-simplex t0345 A2.svg	80px]]

t0,1,2,6{3,3,3,3,3,3}
Hexicantitruncated 7-simplex	[[File:7-simplex t0126.svg	80px]]	[[File:7-simplex t0126 A6.svg	80px]]	[[File:7-simplex t0126 A5.svg	80px]]	[[File:7-simplex t0126 A4.svg	80px]]	[[File:7-simplex t0126 A3.svg	80px]]	[[File:7-simplex t0126 A2.svg	80px]]

t0,1,3,6{3,3,3,3,3,3}
Hexiruncitruncated 7-simplex	[[File:7-simplex t0136.svg	80px]]	[[File:7-simplex t0136 A6.svg	80px]]	[[File:7-simplex t0136 A5.svg	80px]]	[[File:7-simplex t0136 A4.svg	80px]]	[[File:7-simplex t0136 A3.svg	80px]]	[[File:7-simplex t0136 A2.svg	80px]]

t0,2,3,6{3,3,3,3,3,3}
Hexiruncicantellated 7-simplex	[[File:7-simplex t0236.svg	80px]]	[[File:7-simplex t0236 A6.svg	80px]]	[[File:7-simplex t0236 A5.svg	80px]]	[[File:7-simplex t0236 A4.svg	80px]]	[[File:7-simplex t0236 A3.svg	80px]]	[[File:7-simplex t0236 A2.svg	80px]]

t0,1,4,6{3,3,3,3,3,3}
Hexisteritruncated 7-simplex	[[File:7-simplex t0146.svg	80px]]	[[File:7-simplex t0146 A6.svg	80px]]	[[File:7-simplex t0146 A5.svg	80px]]	[[File:7-simplex t0146 A4.svg	80px]]	[[File:7-simplex t0146 A3.svg	80px]]	[[File:7-simplex t0146 A2.svg	80px]]

t0,2,4,6{3,3,3,3,3,3}
Hexistericantellated 7-simplex	[[File:7-simplex t0246.svg	80px]]	[[File:7-simplex t0246 A6.svg	80px]]	[[File:7-simplex t0246 A5.svg	80px]]	[[File:7-simplex t0246 A4.svg	80px]]	[[File:7-simplex t0246 A3.svg	80px]]	[[File:7-simplex t0246 A2.svg	80px]]

t0,1,5,6{3,3,3,3,3,3}
Hexipentitruncated 7-simplex	[[File:7-simplex t0156.svg	80px]]	[[File:7-simplex t0156 A6.svg	80px]]	[[File:7-simplex t0156 A5.svg	80px]]	[[File:7-simplex t0156 A4.svg	80px]]	[[File:7-simplex t0156 A3.svg	80px]]	[[File:7-simplex t0156 A2.svg	80px]]

t0,1,2,3,4{3,3,3,3,3,3}
Steriruncicantitruncated 7-simplex	[[File:7-simplex t01234.svg	80px]]	[[File:7-simplex t01234 A6.svg	80px]]	[[File:7-simplex t01234 A5.svg	80px]]	[[File:7-simplex t01234 A4.svg	80px]]	[[File:7-simplex t01234 A3.svg	80px]]	[[File:7-simplex t01234 A2.svg	80px]]

t0,1,2,3,5{3,3,3,3,3,3}
Pentiruncicantitruncated 7-simplex	[[File:7-simplex t01235.svg	80px]]	[[File:7-simplex t01235 A6.svg	80px]]	[[File:7-simplex t01235 A5.svg	80px]]	[[File:7-simplex t01235 A4.svg	80px]]	[[File:7-simplex t01235 A3.svg	80px]]	[[File:7-simplex t01235 A2.svg	80px]]

t0,1,2,4,5{3,3,3,3,3,3}
Pentistericantitruncated 7-simplex	[[File:7-simplex t01245.svg	80px]]	[[File:7-simplex t01245 A6.svg	80px]]	[[File:7-simplex t01245 A5.svg	80px]]	[[File:7-simplex t01245 A4.svg	80px]]	[[File:7-simplex t01245 A3.svg	80px]]	[[File:7-simplex t01245 A2.svg	80px]]

t0,1,3,4,5{3,3,3,3,3,3}
Pentisteriruncitruncated 7-simplex	[[File:7-simplex t01345.svg	80px]]	[[File:7-simplex t01345 A6.svg	80px]]	[[File:7-simplex t01345 A5.svg	80px]]	[[File:7-simplex t01345 A4.svg	80px]]	[[File:7-simplex t01345 A3.svg	80px]]	[[File:7-simplex t01345 A2.svg	80px]]

t0,2,3,4,5{3,3,3,3,3,3}
Pentisteriruncicantellated 7-simplex	[[File:7-simplex t02345.svg	80px]]	[[File:7-simplex t02345 A6.svg	80px]]	[[File:7-simplex t02345 A5.svg	80px]]	[[File:7-simplex t02345 A4.svg	80px]]	[[File:7-simplex t02345 A3.svg	80px]]	[[File:7-simplex t02345 A2.svg	80px]]

t1,2,3,4,5{3,3,3,3,3,3}
Bisteriruncicantitruncated 7-simplex	[[File:7-simplex t12345.svg	80px]]	[[File:7-simplex t12345 A6.svg	80px]]	[[File:7-simplex t12345 A5.svg	80px]]	[[File:7-simplex t12345 A4.svg	80px]]	[[File:7-simplex t12345 A3.svg	80px]]	[[File:7-simplex t12345 A2.svg	80px]]

t0,1,2,3,6{3,3,3,3,3,3}
Hexiruncicantitruncated 7-simplex	[[File:7-simplex t01236.svg	80px]]	[[File:7-simplex t01236 A6.svg	80px]]	[[File:7-simplex t01236 A5.svg	80px]]	[[File:7-simplex t01236 A4.svg	80px]]	[[File:7-simplex t01236 A3.svg	80px]]	[[File:7-simplex t01236 A2.svg	80px]]

t0,1,2,4,6{3,3,3,3,3,3}
Hexistericantitruncated 7-simplex	[[File:7-simplex t01246.svg	80px]]	[[File:7-simplex t01246 A6.svg	80px]]	[[File:7-simplex t01246 A5.svg	80px]]	[[File:7-simplex t01246 A4.svg	80px]]	[[File:7-simplex t01246 A3.svg	80px]]	[[File:7-simplex t01246 A2.svg	80px]]

t0,1,3,4,6{3,3,3,3,3,3}
Hexisteriruncitruncated 7-simplex	[[File:7-simplex t01346.svg	80px]]	[[File:7-simplex t01346 A6.svg	80px]]	[[File:7-simplex t01346 A5.svg	80px]]	[[File:7-simplex t01346 A4.svg	80px]]	[[File:7-simplex t01346 A3.svg	80px]]	[[File:7-simplex t01346 A2.svg	80px]]

t0,2,3,4,6{3,3,3,3,3,3}
Hexisteriruncicantellated 7-simplex	[[File:7-simplex t02346.svg	80px]]	[[File:7-simplex t02346 A6.svg	80px]]	[[File:7-simplex t02346 A5.svg	80px]]	[[File:7-simplex t02346 A4.svg	80px]]	[[File:7-simplex t02346 A3.svg	80px]]	[[File:7-simplex t02346 A2.svg	80px]]

t0,1,2,5,6{3,3,3,3,3,3}
Hexipenticantitruncated 7-simplex	[[File:7-simplex t01256.svg	80px]]	[[File:7-simplex t01256 A6.svg	80px]]	[[File:7-simplex t01256 A5.svg	80px]]	[[File:7-simplex t01256 A4.svg	80px]]	[[File:7-simplex t01256 A3.svg	80px]]	[[File:7-simplex t01256 A2.svg	80px]]

t0,1,3,5,6{3,3,3,3,3,3}
Hexipentiruncitruncated 7-simplex	[[File:7-simplex t01356.svg	80px]]	[[File:7-simplex t01356 A6.svg	80px]]	[[File:7-simplex t01356 A5.svg	80px]]	[[File:7-simplex t01356 A4.svg	80px]]	[[File:7-simplex t01356 A3.svg	80px]]	[[File:7-simplex t01356 A2.svg	80px]]

t0,1,2,3,4,5{3,3,3,3,3,3}
Pentisteriruncicantitruncated 7-simplex	[[File:7-simplex t012345.svg	80px]]	[[File:7-simplex t012345 A6.svg	80px]]	[[File:7-simplex t012345 A5.svg	80px]]	[[File:7-simplex t012345 A4.svg	80px]]	[[File:7-simplex t012345 A3.svg	80px]]	[[File:7-simplex t012345 A2.svg	80px]]

t0,1,2,3,4,6{3,3,3,3,3,3}
Hexisteriruncicantitruncated 7-simplex	[[File:7-simplex t012346.svg	80px]]	[[File:7-simplex t012346 A6.svg	80px]]	[[File:7-simplex t012346 A5.svg	80px]]	[[File:7-simplex t012346 A4.svg	80px]]	[[File:7-simplex t012346 A3.svg	80px]]	[[File:7-simplex t012346 A2.svg	80px]]

t0,1,2,3,5,6{3,3,3,3,3,3}
Hexipentiruncicantitruncated 7-simplex	[[File:7-simplex t012356.svg	80px]]	[[File:7-simplex t012356 A6.svg	80px]]	[[File:7-simplex t012356 A5.svg	80px]]	[[File:7-simplex t012356 A4.svg	80px]]	[[File:7-simplex t012356 A3.svg	80px]]	[[File:7-simplex t012356 A2.svg	80px]]

t0,1,2,4,5,6{3,3,3,3,3,3}
Hexipentistericantitruncated 7-simplex	[[File:7-simplex t012456.svg	80px]]	[[File:7-simplex t012456 A6.svg	80px]]	[[File:7-simplex t012456 A5.svg	80px]]	[[File:7-simplex t012456 A4.svg	80px]]	[[File:7-simplex t012456 A3.svg	80px]]	[[File:7-simplex t012456 A2.svg	80px]]

t0,1,2,3,4,5,6{3,3,3,3,3,3}
Omnitruncated 7-simplex	[[File:7-simplex t0123456.svg	80px]]	[[File:7-simplex t0123456 A6.svg	80px]]	[[File:7-simplex t0123456 A5.svg	80px]]	[[File:7-simplex t0123456 A4.svg	80px]]	[[File:7-simplex t0123456 A3.svg	80px]]	[[File:7-simplex t0123456 A2.svg	80px]]

References

H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
- (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966

Notes

References

"Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter".

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