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# Polytope of Type {8,15}

Atlas Canonical Name : {8,15}*960a
if this polytope has a name.
Group : SmallGroup(960,6311)
Rank : 3
Schlafli Type : {8,15}
Number of vertices, edges, etc : 32, 240, 60
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,15,2} of size 1920
Vertex Figure Of :
{2,8,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {4,15}*240
5-fold quotients : {8,3}*192
8-fold quotients : {4,15}*120
16-fold quotients : {2,15}*60
20-fold quotients : {4,3}*48
40-fold quotients : {4,3}*24
48-fold quotients : {2,5}*20
80-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,15}*1920a, {8,30}*1920a, {8,30}*1920d
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)(18,26)
(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)(37,48)
(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)
(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77);;
s1 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,65)(18,66)(19,68)(20,67)
(21,74)(22,73)(23,75)(24,76)(25,70)(26,69)(27,71)(28,72)(29,77)(30,78)(31,80)
(32,79)(33,49)(34,50)(35,52)(36,51)(37,58)(38,57)(39,59)(40,60)(41,54)(42,53)
(43,55)(44,56)(45,61)(46,62)(47,64)(48,63);;
s2 := ( 1,25)( 2,28)( 3,27)( 4,26)( 5,23)( 6,22)( 7,21)( 8,24)( 9,17)(10,20)
(11,19)(12,18)(13,29)(14,32)(15,31)(16,30)(33,73)(34,76)(35,75)(36,74)(37,71)
(38,70)(39,69)(40,72)(41,65)(42,68)(43,67)(44,66)(45,77)(46,80)(47,79)(48,78)
(49,57)(50,60)(51,59)(52,58)(53,55)(62,64);;
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*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(80)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)
(18,26)(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)
(37,48)(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)
(56,61)(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77);
s1 := Sym(80)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,65)(18,66)(19,68)
(20,67)(21,74)(22,73)(23,75)(24,76)(25,70)(26,69)(27,71)(28,72)(29,77)(30,78)
(31,80)(32,79)(33,49)(34,50)(35,52)(36,51)(37,58)(38,57)(39,59)(40,60)(41,54)
(42,53)(43,55)(44,56)(45,61)(46,62)(47,64)(48,63);
s2 := Sym(80)!( 1,25)( 2,28)( 3,27)( 4,26)( 5,23)( 6,22)( 7,21)( 8,24)( 9,17)
(10,20)(11,19)(12,18)(13,29)(14,32)(15,31)(16,30)(33,73)(34,76)(35,75)(36,74)
(37,71)(38,70)(39,69)(40,72)(41,65)(42,68)(43,67)(44,66)(45,77)(46,80)(47,79)
(48,78)(49,57)(50,60)(51,59)(52,58)(53,55)(62,64);
poly := sub<Sym(80)|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*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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