# 7-simpleks

Skoči na: navigacija, iskanje
pravilni oktaekson
(7-simpleks)

Ortogonalna projekcija
v Petrijevem mnogokotniku
vrsta pravilni 7-politop
družina simpleks
Schläflijev simbol {3,3,3,3,3,3}
Coxeter-Dynkinov diagram
6-stranske ploskve 8 6-simpleks
5-stranske ploskve 28 5-simpleks
4-stranske ploskve 56 5-celica
Celice 70 tetraeder
Stranske ploskve 56 trikotnik
Robovi 28
Oglišča 8
Slika oglišč 6-simpleks
Petrijev mnogokotnik osemkotnik
Coxeterjeva grupa A7 [3,3,3,3,3,3]
Dualnost sebi dualni
Lastnost konveksni

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 diederski kot cos−1(1/7)kar je približno 81,79°.

## Koordinate oglišč

$\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ \sqrt{1/6},\ \sqrt{1/3},\ \pm1\right)$
$\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ \sqrt{1/6},\ -2\sqrt{1/3},\ 0\right)$
$\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ \sqrt{1/10},\ -\sqrt{3/2},\ 0,\ 0\right)$
$\left(\sqrt{1/28},\ \sqrt{1/21},\ \sqrt{1/15},\ -2\sqrt{2/5},\ 0,\ 0,\ 0\right)$
$\left(\sqrt{1/28},\ \sqrt{1/21},\ -\sqrt{5/3},\ 0,\ 0,\ 0,\ 0\right)$
$\left(\sqrt{1/28},\ -\sqrt{12/7},\ 0,\ 0,\ 0,\ 0,\ 0\right)$
$\left(-\sqrt{7/4},\ 0,\ 0,\ 0,\ 0,\ 0,\ 0\right)$

## Sorodni politopi

 t0 t1 t2 t3 t0,1 t0,2 t1,2 t0,3 t1,3 t2,3 t0,4 t1,4 t2,4 t0,5 t1,5 t0,6 t0,1,2 t0,1,3 t0,2,3 t1,2,3 t0,1,4 t0,2,4 t1,2,4 t0,3,4 t1,3,4 t2,3,4 t0,1,5 t0,2,5 t1,2,5 t0,3,5 t1,3,5 t0,4,5 t0,1,6 t0,2,6 t0,3,6 t0,1,2,3 t0,1,2,4 t0,1,3,4 t0,2,3,4 t1,2,3,4 t0,1,2,5 t0,1,3,5 t0,2,3,5 t1,2,3,5 t0,1,4,5 t0,2,4,5 t1,2,4,5 t0,3,4,5 t0,1,2,6 t0,1,3,6 t0,2,3,6 t0,1,4,6 t0,2,4,6 t0,1,5,6 t0,1,2,3,4 t0,1,2,3,5 t0,1,2,4,5 t0,1,3,4,5 t0,2,3,4,5 t1,2,3,4,5 t0,1,2,3,6 t0,1,2,4,6 t0,1,3,4,6 t0,2,3,4,6 t0,1,2,5,6 t0,1,3,5,6 t0,1,2,3,4,5 t0,1,2,3,4,6 t0,1,2,3,5,6 t0,1,2,4,5,6 t0,1,2,3,4,5,6