# Polytope of Type {24,10}

Atlas Canonical Name : {24,10}*1920f
if this polytope has a name.
Group : SmallGroup(1920,240882)
Rank : 3
Schlafli Type : {24,10}
Number of vertices, edges, etc : 96, 480, 40
Order of s0s1s2 : 40
Order of s0s1s2s1 : 20
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 : {12,10}*960c
4-fold quotients : {12,10}*480c, {12,10}*480d, {6,10}*480c
8-fold quotients : {3,10}*240, {6,5}*240b, {6,10}*240c, {6,10}*240d, {6,10}*240e, {6,10}*240f
16-fold quotients : {3,5}*120, {3,10}*120a, {3,10}*120b, {6,5}*120b, {6,5}*120c
32-fold quotients : {3,5}*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 := ( 1,55)( 2,93)( 3,56)( 4,66)( 5,65)( 6,79)( 7,90)( 8,96)( 9,95)(10,67)
(11,57)(12,76)(13,70)(14,77)(15,86)(16,91)(17,78)(18,88)(19,89)(20,50)(21,59)
(22,71)(23,82)(24,81)(25,87)(26,80)(27,94)(28,85)(29,58)(30,73)(31,53)(32,68)
(33,83)(34,72)(35,92)(36,69)(37,84)(38,60)(39,51)(40,74)(41,75)(42,62)(43,49)
(44,61)(45,54)(46,52)(47,64)(48,63);;
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, s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*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)!( 1,55)( 2,93)( 3,56)( 4,66)( 5,65)( 6,79)( 7,90)( 8,96)( 9,95)
(10,67)(11,57)(12,76)(13,70)(14,77)(15,86)(16,91)(17,78)(18,88)(19,89)(20,50)
(21,59)(22,71)(23,82)(24,81)(25,87)(26,80)(27,94)(28,85)(29,58)(30,73)(31,53)
(32,68)(33,83)(34,72)(35,92)(36,69)(37,84)(38,60)(39,51)(40,74)(41,75)(42,62)
(43,49)(44,61)(45,54)(46,52)(47,64)(48,63);
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, s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*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