# Polytope of Type {12,15}

Atlas Canonical Name : {12,15}*1440b
if this polytope has a name.
Group : SmallGroup(1440,4642)
Rank : 3
Schlafli Type : {12,15}
Number of vertices, edges, etc : 48, 360, 60
Order of s0s1s2 : 60
Order of s0s1s2s1 : 20
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,15}*720d
3-fold quotients : {12,5}*480
4-fold quotients : {6,15}*360
6-fold quotients : {6,5}*240b
12-fold quotients : {3,5}*120, {6,5}*120b, {6,5}*120c
24-fold quotients : {3,5}*60
120-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 4)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)(11,40)
(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)(28,32)
(33,48)(35,39)(41,47);;
s1 := ( 2,40)( 3,46)( 4,45)( 5,33)( 6, 7)( 8,25)( 9,22)(12,21)(13,44)(15,30)
(16,26)(18,34)(19,38)(20,27)(23,47)(24,48)(29,41)(32,35)(36,39)(42,43)
(50,51);;
s2 := ( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)(17,33)
(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(49,50);;
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*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*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*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(51)!( 1, 4)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)
(11,40)(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)
(28,32)(33,48)(35,39)(41,47);
s1 := Sym(51)!( 2,40)( 3,46)( 4,45)( 5,33)( 6, 7)( 8,25)( 9,22)(12,21)(13,44)
(15,30)(16,26)(18,34)(19,38)(20,27)(23,47)(24,48)(29,41)(32,35)(36,39)(42,43)
(50,51);
s2 := Sym(51)!( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)
(17,33)(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(49,50);
poly := sub<Sym(51)|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*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*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*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope