Polytope of Type {12,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,30}*720d
if this polytope has a name.
Group : SmallGroup(720,793)
Rank : 3
Schlafli Type : {12,30}
Number of vertices, edges, etc : 12, 180, 30
Order of s0s1s2 : 15
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,30,2} of size 1440
Vertex Figure Of :
{2,12,30} of size 1440
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,30}*240c
5-fold quotients : {12,6}*144d
6-fold quotients : {4,15}*120
15-fold quotients : {4,6}*48b
30-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,30}*1440a
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)
(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(29,51)(30,52)(31,49)
(32,50)(33,55)(34,56)(35,53)(36,54)(37,59)(38,60)(39,57)(40,58);;
s1 := ( 1,21)( 2,23)( 3,22)( 4,24)( 5,37)( 6,39)( 7,38)( 8,40)( 9,33)(10,35)
(11,34)(12,36)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(42,43)
(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56);;
s2 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,25)
(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)(43,47)
(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);;
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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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(60)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)
(18,20)(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(29,51)(30,52)
(31,49)(32,50)(33,55)(34,56)(35,53)(36,54)(37,59)(38,60)(39,57)(40,58);
s1 := Sym(60)!( 1,21)( 2,23)( 3,22)( 4,24)( 5,37)( 6,39)( 7,38)( 8,40)( 9,33)
(10,35)(11,34)(12,36)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)
(42,43)(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56);
s2 := Sym(60)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)
(21,25)(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)
(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);
poly := sub<Sym(60)|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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```
References : None.
to this polytope