Iz Wikipedije, proste enciklopedije
pravilni oktaekson (7-simpleks)
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/7-simplex_t0.svg/280px-7-simplex_t0.svg.png) Ortogonalna projekcija v Petriejevem mnogokotniku
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vrsta |
pravilni 7-politop
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družina |
simpleks
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Schläflijev simbol |
{3,3,3,3,3,3}
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Coxeter-Dinkinov diagram |
![](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/c/c3/CDel_3.png)
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6-stranske ploskve |
8 6-simpleks
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5-stranske ploskve |
28 5-simpleks
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4-stranske ploskve |
56 5-celica
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celice |
70 tetraeder
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stranske ploskve |
56 trikotnik
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robovi |
28
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oglišča |
8
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slika oglišč |
6-simpleks
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Petriejev mnogokotnik |
osemkotnik
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Coxeterjeva grupa |
A7 [3,3,3,3,3,3]
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dualnost |
sebidualni
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značilnosti |
konveksni
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7-simpleks (tudi oktaekson ali oktatop) je v 7-razsežni geometriji sebi dualni pravilni 7-politop. Ima 8 oglišč, 28 robov, 56 trikotnih stranskih ploskev, 70 tetraederskih celic, 56 5-celic s 5 stranskimi ploskvami, 28 5-simpleksov s 6 stranskimi ploskvami in 8 6-simpleksov s 7 stranskimi ploskvami.
Ima diedrski kot cos−1(1/7)kar je približno 81,79°.
![{\displaystyle \left({\sqrt {1/28}},\ {\sqrt {1/21}},\ {\sqrt {1/15}},\ {\sqrt {1/10}},\ {\sqrt {1/6}},\ {\sqrt {1/3}},\ \pm 1\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f6253789eb0cbbaa7d108eab6aeb20cd3963158f)
![{\displaystyle \left({\sqrt {1/28}},\ {\sqrt {1/21}},\ {\sqrt {1/15}},\ {\sqrt {1/10}},\ {\sqrt {1/6}},\ -2{\sqrt {1/3}},\ 0\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49150a300e748c14b10e9e1002ca83dd85e2497c)
![{\displaystyle \left({\sqrt {1/28}},\ {\sqrt {1/21}},\ {\sqrt {1/15}},\ {\sqrt {1/10}},\ -{\sqrt {3/2}},\ 0,\ 0\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/009e191c98774b93b03b2139adf9a322ff9e3da9)
![{\displaystyle \left({\sqrt {1/28}},\ {\sqrt {1/21}},\ {\sqrt {1/15}},\ -2{\sqrt {2/5}},\ 0,\ 0,\ 0\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c87cb368f35a622dd64c2b96874ec2691bb845b7)
![{\displaystyle \left({\sqrt {1/28}},\ {\sqrt {1/21}},\ -{\sqrt {5/3}},\ 0,\ 0,\ 0,\ 0\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/228ecedf6564247dac820551ee8087ed539c50c9)
![{\displaystyle \left({\sqrt {1/28}},\ -{\sqrt {12/7}},\ 0,\ 0,\ 0,\ 0,\ 0\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7b70bd304b4bf5e280fbafb57c4201a5e87b3144)
![{\displaystyle \left(-{\sqrt {7/4}},\ 0,\ 0,\ 0,\ 0,\ 0,\ 0\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5c37ff3a08d5ecf1c007a2f7a73c763cf2f04cb)
![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/7-simplex_t0.svg/80px-7-simplex_t0.svg.png) t0
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![](//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/7-simplex_t1.svg/80px-7-simplex_t1.svg.png) t1
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/7-simplex_t2.svg/80px-7-simplex_t2.svg.png) t2
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/67/7-simplex_t3.svg/80px-7-simplex_t3.svg.png) t3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/7-simplex_t01.svg/80px-7-simplex_t01.svg.png) t0,1
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/7-simplex_t02.svg/80px-7-simplex_t02.svg.png) t0,2
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/03/7-simplex_t12.svg/80px-7-simplex_t12.svg.png) t1,2
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/67/7-simplex_t03.svg/80px-7-simplex_t03.svg.png) t0,3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/7-simplex_t13.svg/80px-7-simplex_t13.svg.png) t1,3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/44/7-simplex_t23.svg/80px-7-simplex_t23.svg.png) t2,3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/7-simplex_t04.svg/80px-7-simplex_t04.svg.png) t0,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/7-simplex_t14.svg/80px-7-simplex_t14.svg.png) t1,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/74/7-simplex_t24.svg/80px-7-simplex_t24.svg.png) t2,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/7-simplex_t05.svg/80px-7-simplex_t05.svg.png) t0,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/7-simplex_t15.svg/80px-7-simplex_t15.svg.png) t1,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/9/97/7-simplex_t06.svg/80px-7-simplex_t06.svg.png) t0,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/7-simplex_t012.svg/80px-7-simplex_t012.svg.png) t0,1,2
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/49/7-simplex_t013.svg/80px-7-simplex_t013.svg.png) t0,1,3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/78/7-simplex_t023.svg/80px-7-simplex_t023.svg.png) t0,2,3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/7-simplex_t123.svg/80px-7-simplex_t123.svg.png) t1,2,3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/79/7-simplex_t014.svg/80px-7-simplex_t014.svg.png) t0,1,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/7-simplex_t024.svg/80px-7-simplex_t024.svg.png) t0,2,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/60/7-simplex_t124.svg/80px-7-simplex_t124.svg.png) t1,2,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/06/7-simplex_t034.svg/80px-7-simplex_t034.svg.png) t0,3,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/2/22/7-simplex_t134.svg/80px-7-simplex_t134.svg.png) t1,3,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/7-simplex_t234.svg/80px-7-simplex_t234.svg.png) t2,3,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/1/17/7-simplex_t015.svg/80px-7-simplex_t015.svg.png) t0,1,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/05/7-simplex_t025.svg/80px-7-simplex_t025.svg.png) t0,2,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/7-simplex_t125.svg/80px-7-simplex_t125.svg.png) t1,2,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/7-simplex_t035.svg/80px-7-simplex_t035.svg.png) t0,3,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/7-simplex_t135.svg/80px-7-simplex_t135.svg.png) t1,3,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/7-simplex_t045.svg/80px-7-simplex_t045.svg.png) t0,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/7-simplex_t016.svg/80px-7-simplex_t016.svg.png) t0,1,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/7-simplex_t026.svg/80px-7-simplex_t026.svg.png) t0,2,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/7-simplex_t036.svg/80px-7-simplex_t036.svg.png) t0,3,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/63/7-simplex_t0123.svg/80px-7-simplex_t0123.svg.png) t0,1,2,3
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/7-simplex_t0124.svg/80px-7-simplex_t0124.svg.png) t0,1,2,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/7-simplex_t0134.svg/80px-7-simplex_t0134.svg.png) t0,1,3,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/5/53/7-simplex_t0234.svg/80px-7-simplex_t0234.svg.png) t0,2,3,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/7-simplex_t1234.svg/80px-7-simplex_t1234.svg.png) t1,2,3,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/7-simplex_t0125.svg/80px-7-simplex_t0125.svg.png) t0,1,2,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/6/61/7-simplex_t0135.svg/80px-7-simplex_t0135.svg.png) t0,1,3,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/5/53/7-simplex_t0235.svg/80px-7-simplex_t0235.svg.png) t0,2,3,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/7-simplex_t1235.svg/80px-7-simplex_t1235.svg.png) t1,2,3,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/7-simplex_t0145.svg/80px-7-simplex_t0145.svg.png) t0,1,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/2/23/7-simplex_t0245.svg/80px-7-simplex_t0245.svg.png) t0,2,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/3/30/7-simplex_t1245.svg/80px-7-simplex_t1245.svg.png) t1,2,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/da/7-simplex_t0345.svg/80px-7-simplex_t0345.svg.png) t0,3,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/80/7-simplex_t0126.svg/80px-7-simplex_t0126.svg.png) t0,1,2,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/7-simplex_t0136.svg/80px-7-simplex_t0136.svg.png) t0,1,3,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/7-simplex_t0236.svg/80px-7-simplex_t0236.svg.png) t0,2,3,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/7-simplex_t0146.svg/80px-7-simplex_t0146.svg.png) t0,1,4,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/7-simplex_t0246.svg/80px-7-simplex_t0246.svg.png) t0,2,4,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/7-simplex_t0156.svg/80px-7-simplex_t0156.svg.png) t0,1,5,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/82/7-simplex_t01234.svg/80px-7-simplex_t01234.svg.png) t0,1,2,3,4
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![](//upload.wikimedia.org/wikipedia/commons/thumb/5/58/7-simplex_t01235.svg/80px-7-simplex_t01235.svg.png) t0,1,2,3,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/7-simplex_t01245.svg/80px-7-simplex_t01245.svg.png) t0,1,2,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/02/7-simplex_t01345.svg/80px-7-simplex_t01345.svg.png) t0,1,3,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/2/20/7-simplex_t02345.svg/80px-7-simplex_t02345.svg.png) t0,2,3,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/da/7-simplex_t12345.svg/80px-7-simplex_t12345.svg.png) t1,2,3,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/7-simplex_t01236.svg/80px-7-simplex_t01236.svg.png) t0,1,2,3,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/7-simplex_t01246.svg/80px-7-simplex_t01246.svg.png) t0,1,2,4,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/1/19/7-simplex_t01346.svg/80px-7-simplex_t01346.svg.png) t0,1,3,4,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/7-simplex_t02346.svg/80px-7-simplex_t02346.svg.png) t0,2,3,4,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/7-simplex_t01256.svg/80px-7-simplex_t01256.svg.png) t0,1,2,5,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/7-simplex_t01356.svg/80px-7-simplex_t01356.svg.png) t0,1,3,5,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/4/42/7-simplex_t012345.svg/80px-7-simplex_t012345.svg.png) t0,1,2,3,4,5
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![](//upload.wikimedia.org/wikipedia/commons/thumb/a/af/7-simplex_t012346.svg/80px-7-simplex_t012346.svg.png) t0,1,2,3,4,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/df/7-simplex_t012356.svg/80px-7-simplex_t012356.svg.png) t0,1,2,3,5,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/7-simplex_t012456.svg/80px-7-simplex_t012456.svg.png) t0,1,2,4,5,6
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![](//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/7-simplex_t0123456.svg/80px-7-simplex_t0123456.svg.png) t0,1,2,3,4,5,6
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