# Polytope of Type {40,10}

Atlas Canonical Name : {40,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240882)
Rank : 3
Schlafli Type : {40,10}
Number of vertices, edges, etc : 96, 480, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {20,10}*960a
4-fold quotients : {20,10}*480a, {20,10}*480b, {10,10}*480
8-fold quotients : {5,10}*240, {10,5}*240, {10,10}*240a, {10,10}*240b, {10,10}*240c, {10,10}*240d
16-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b, {10,5}*120a, {10,5}*120b
32-fold quotients : {5,5}*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 := ( 2,39)( 3,10)( 6,42)( 7,38)( 8,21)( 9,29)(11,20)(13,24)(14,41)(15,40)
(16,30)(17,46)(18,43)(19,32)(23,35)(25,48)(26,45)(27,37)(28,31)(36,47)(49,63)
(50,88)(51,84)(52,64)(53,75)(54,60)(55,93)(56,78)(57,85)(58,74)(59,62)(65,95)
(66,96)(67,90)(68,73)(69,80)(70,81)(76,89)(77,87)(82,92);;
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*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!( 2,39)( 3,10)( 6,42)( 7,38)( 8,21)( 9,29)(11,20)(13,24)(14,41)
(15,40)(16,30)(17,46)(18,43)(19,32)(23,35)(25,48)(26,45)(27,37)(28,31)(36,47)
(49,63)(50,88)(51,84)(52,64)(53,75)(54,60)(55,93)(56,78)(57,85)(58,74)(59,62)
(65,95)(66,96)(67,90)(68,73)(69,80)(70,81)(76,89)(77,87)(82,92);
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*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope