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# Polytope of Type {40,6}

Atlas Canonical Name : {40,6}*1920h
if this polytope has a name.
Group : SmallGroup(1920,240882)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 160, 480, 24
Order of s0s1s2 : 40
Order of s0s1s2s1 : 20
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {20,6}*960c
4-fold quotients : {20,6}*480a, {20,6}*480b, {10,6}*480c
8-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
16-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
32-fold quotients : {5,3}*60
120-fold quotients : {4,2}*16
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1,61)( 2,53)( 3,70)( 4,71)( 5,72)( 6,50)( 7,58)( 8,60)( 9,49)(10,81)
(11,82)(12,83)(13,87)(14,55)(15,56)(16,57)(17,51)(18,68)(19,52)(20,92)(21,54)
(22,94)(23,69)(24,77)(25,65)(26,66)(27,67)(28,59)(29,63)(30,85)(31,62)(32,64)
(33,86)(34,79)(35,80)(36,76)(37,90)(38,74)(39,75)(40,78)(41,93)(42,88)(43,73)
(44,91)(45,96)(46,84)(47,89)(48,95);;
s1 := ( 1,51)( 2,55)( 3,52)( 4,59)( 5,58)( 6,62)( 7,56)( 8,66)( 9,65)(10,60)
(11,53)(12,68)(13,70)(14,63)(15,74)(16,73)(17,67)(18,57)(19,76)(20,49)(21,79)
(22,71)(23,82)(24,81)(25,75)(26,64)(27,84)(28,50)(29,86)(30,89)(31,77)(32,91)
(33,83)(34,72)(35,92)(36,54)(37,93)(38,80)(39,94)(40,95)(41,85)(42,96)(43,87)
(44,61)(45,90)(46,69)(47,78)(48,88);;
s2 := ( 1,13)( 2, 9)( 3,33)( 4,23)( 5,24)( 6,37)( 8,19)(10,22)(11,44)(12,35)
(14,47)(15,42)(16,40)(20,34)(25,45)(26,41)(27,30)(31,43)(36,48)(38,46)(49,53)
(50,90)(52,60)(55,89)(56,88)(57,78)(61,87)(62,73)(65,96)(66,93)(67,85)(69,71)
(70,86)(72,77)(74,84)(76,95)(79,92)(80,83)(81,94)(82,91);;
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,
s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope