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# Polytope of Type {8,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,48}*768b
if this polytope has a name.
Group : SmallGroup(768,82982)
Rank : 3
Schlafli Type : {8,48}
Number of vertices, edges, etc : 8, 192, 48
Order of s0s1s2 : 48
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,24}*384d
3-fold quotients : {8,16}*256b
4-fold quotients : {4,24}*192b, {8,12}*192a
6-fold quotients : {8,8}*128c
8-fold quotients : {4,12}*96a, {8,6}*96
12-fold quotients : {8,4}*64a, {4,8}*64b
16-fold quotients : {2,12}*48, {4,6}*48a
24-fold quotients : {4,4}*32, {8,2}*32
32-fold quotients : {2,6}*24
48-fold quotients : {2,4}*16, {4,2}*16
64-fold quotients : {2,3}*12
96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,58)( 8,59)( 9,60)(10,55)
(11,56)(12,57)(13,67)(14,68)(15,69)(16,70)(17,71)(18,72)(19,61)(20,62)(21,63)
(22,64)(23,65)(24,66)(25,73)(26,74)(27,75)(28,76)(29,77)(30,78)(31,82)(32,83)
(33,84)(34,79)(35,80)(36,81)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)
(44,86)(45,87)(46,88)(47,89)(48,90);;
s1 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,22)(14,24)(15,23)(16,19)(17,21)
(18,20)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)
(35,45)(36,44)(50,51)(53,54)(55,58)(56,60)(57,59)(61,70)(62,72)(63,71)(64,67)
(65,69)(66,68)(73,85)(74,87)(75,86)(76,88)(77,90)(78,89)(79,94)(80,96)(81,95)
(82,91)(83,93)(84,92);;
s2 := ( 1,26)( 2,25)( 3,27)( 4,29)( 5,28)( 6,30)( 7,35)( 8,34)( 9,36)(10,32)
(11,31)(12,33)(13,47)(14,46)(15,48)(16,44)(17,43)(18,45)(19,41)(20,40)(21,42)
(22,38)(23,37)(24,39)(49,74)(50,73)(51,75)(52,77)(53,76)(54,78)(55,83)(56,82)
(57,84)(58,80)(59,79)(60,81)(61,95)(62,94)(63,96)(64,92)(65,91)(66,93)(67,89)
(68,88)(69,90)(70,86)(71,85)(72,87);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope