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# Polytope of Type {76,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {76,6}*912b
if this polytope has a name.
Group : SmallGroup(912,207)
Rank : 3
Schlafli Type : {76,6}
Number of vertices, edges, etc : 76, 228, 6
Order of s0s1s2 : 57
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{76,6,2} of size 1824
Vertex Figure Of :
{2,76,6} of size 1824
Quotients (Maximal Quotients in Boldface) :
19-fold quotients : {4,6}*48b
38-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {76,6}*1824
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 4)( 5,75)( 6,76)( 7,73)( 8,74)( 9,71)(10,72)(11,69)(12,70)
(13,67)(14,68)(15,65)(16,66)(17,63)(18,64)(19,61)(20,62)(21,59)(22,60)(23,57)
(24,58)(25,55)(26,56)(27,53)(28,54)(29,51)(30,52)(31,49)(32,50)(33,47)(34,48)
(35,45)(36,46)(37,43)(38,44)(39,41)(40,42);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,73)(10,75)(11,74)(12,76)(13,69)(14,71)
(15,70)(16,72)(17,65)(18,67)(19,66)(20,68)(21,61)(22,63)(23,62)(24,64)(25,57)
(26,59)(27,58)(28,60)(29,53)(30,55)(31,54)(32,56)(33,49)(34,51)(35,50)(36,52)
(37,45)(38,47)(39,46)(40,48)(42,43);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40)
(42,44)(46,48)(50,52)(54,56)(58,60)(62,64)(66,68)(70,72)(74,76);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;

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

```
References : None.
to this polytope