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# Polytope of Type {8,6}

Atlas Canonical Name : {8,6}*192b
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 16, 48, 12
Order of s0s1s2 : 12
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{8,6,2} of size 384
{8,6,4} of size 768
{8,6,4} of size 768
{8,6,4} of size 768
{8,6,6} of size 1152
{8,6,6} of size 1152
{8,6,6} of size 1728
{8,6,10} of size 1920
Vertex Figure Of :
{2,8,6} of size 384
{4,8,6} of size 768
{6,8,6} of size 1152
{10,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,3}*96, {4,6}*96
4-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
8-fold quotients : {4,3}*24, {2,6}*24
16-fold quotients : {2,3}*12
24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,12}*384e, {8,6}*384f, {8,12}*384h
3-fold covers : {8,18}*576b, {24,6}*576b, {24,6}*576e
4-fold covers : {8,6}*768d, {8,6}*768e, {8,6}*768f, {8,24}*768i, {8,24}*768j, {8,6}*768j, {8,24}*768n, {8,12}*768p, {8,24}*768p, {8,12}*768s
5-fold covers : {40,6}*960e, {8,30}*960b
6-fold covers : {8,36}*1152e, {8,18}*1152f, {8,36}*1152h, {24,12}*1152k, {24,12}*1152l, {24,12}*1152m, {24,6}*1152d, {24,6}*1152l, {24,12}*1152v
7-fold covers : {56,6}*1344c, {8,42}*1344b
9-fold covers : {8,54}*1728b, {72,6}*1728c, {24,18}*1728b, {24,6}*1728b, {24,18}*1728e, {24,6}*1728e, {24,6}*1728f
10-fold covers : {40,12}*1920f, {40,6}*1920b, {40,12}*1920h, {8,60}*1920e, {8,30}*1920f, {8,60}*1920h
Permutation Representation (GAP) :
```s0 := ( 1,27)( 2,28)( 3,26)( 4,25)( 5,31)( 6,32)( 7,30)( 8,29)( 9,35)(10,36)
(11,34)(12,33)(13,39)(14,40)(15,38)(16,37)(17,43)(18,44)(19,42)(20,41)(21,47)
(22,48)(23,46)(24,45)(49,75)(50,76)(51,74)(52,73)(53,79)(54,80)(55,78)(56,77)
(57,83)(58,84)(59,82)(60,81)(61,87)(62,88)(63,86)(64,85)(65,91)(66,92)(67,90)
(68,89)(69,95)(70,96)(71,94)(72,93);;
s1 := ( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)(15,24)
(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)(39,47)
(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)(63,72)
(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)(87,95)
(88,96);;
s2 := ( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)(10,50)
(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)(21,71)
(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)(32,85)
(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)(43,91)
(44,92)(45,96)(46,95)(47,94)(48,93);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(96)!( 1,27)( 2,28)( 3,26)( 4,25)( 5,31)( 6,32)( 7,30)( 8,29)( 9,35)
(10,36)(11,34)(12,33)(13,39)(14,40)(15,38)(16,37)(17,43)(18,44)(19,42)(20,41)
(21,47)(22,48)(23,46)(24,45)(49,75)(50,76)(51,74)(52,73)(53,79)(54,80)(55,78)
(56,77)(57,83)(58,84)(59,82)(60,81)(61,87)(62,88)(63,86)(64,85)(65,91)(66,92)
(67,90)(68,89)(69,95)(70,96)(71,94)(72,93);
s1 := Sym(96)!( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)
(15,24)(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)
(39,47)(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)
(63,72)(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)
(87,95)(88,96);
s2 := Sym(96)!( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)
(10,50)(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)
(21,71)(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)
(32,85)(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)
(43,91)(44,92)(45,96)(46,95)(47,94)(48,93);
poly := sub<Sym(96)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope