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# Polytope of Type {12,12}

Atlas Canonical Name : {12,12}*288c
if this polytope has a name.
Group : SmallGroup(288,571)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 12, 72, 12
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,12,2} of size 576
{12,12,4} of size 1152
{12,12,6} of size 1728
{12,12,3} of size 1728
{12,12,6} of size 1728
Vertex Figure Of :
{2,12,12} of size 576
{4,12,12} of size 1152
{4,12,12} of size 1152
{4,12,12} of size 1152
{6,12,12} of size 1728
{6,12,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,6}*144b, {6,12}*144c
3-fold quotients : {12,4}*96a
4-fold quotients : {6,6}*72c
6-fold quotients : {12,2}*48, {6,4}*48a
8-fold quotients : {3,6}*36
9-fold quotients : {4,4}*32
12-fold quotients : {6,2}*24
18-fold quotients : {2,4}*16, {4,2}*16
24-fold quotients : {3,2}*12
36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,24}*576a, {12,12}*576c, {12,24}*576b, {24,12}*576d, {24,12}*576f
3-fold covers : {36,12}*864b, {12,12}*864a, {12,12}*864h
4-fold covers : {24,12}*1152a, {12,24}*1152c, {24,24}*1152c, {24,24}*1152d, {24,24}*1152e, {24,24}*1152l, {48,12}*1152a, {12,48}*1152c, {48,12}*1152d, {12,48}*1152f, {12,12}*1152a, {12,24}*1152d, {24,12}*1152f, {12,12}*1152l, {12,12}*1152m
5-fold covers : {12,60}*1440a, {60,12}*1440c
6-fold covers : {36,24}*1728a, {12,24}*1728a, {36,12}*1728b, {12,12}*1728a, {36,24}*1728b, {12,24}*1728b, {72,12}*1728b, {24,12}*1728c, {72,12}*1728d, {24,12}*1728e, {12,24}*1728o, {24,12}*1728o, {12,24}*1728p, {24,12}*1728p, {12,12}*1728h
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)
(23,27)(24,26)(29,30)(31,34)(32,36)(33,35)(37,64)(38,66)(39,65)(40,70)(41,72)
(42,71)(43,67)(44,69)(45,68)(46,55)(47,57)(48,56)(49,61)(50,63)(51,62)(52,58)
(53,60)(54,59);;
s1 := ( 1,41)( 2,40)( 3,42)( 4,38)( 5,37)( 6,39)( 7,44)( 8,43)( 9,45)(10,50)
(11,49)(12,51)(13,47)(14,46)(15,48)(16,53)(17,52)(18,54)(19,59)(20,58)(21,60)
(22,56)(23,55)(24,57)(25,62)(26,61)(27,63)(28,68)(29,67)(30,69)(31,65)(32,64)
(33,66)(34,71)(35,70)(36,72);;
s2 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)(31,34)
(32,35)(33,36)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)(43,58)(44,59)(45,60)
(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)(54,69);;
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*s2*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(72)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)
(22,25)(23,27)(24,26)(29,30)(31,34)(32,36)(33,35)(37,64)(38,66)(39,65)(40,70)
(41,72)(42,71)(43,67)(44,69)(45,68)(46,55)(47,57)(48,56)(49,61)(50,63)(51,62)
(52,58)(53,60)(54,59);
s1 := Sym(72)!( 1,41)( 2,40)( 3,42)( 4,38)( 5,37)( 6,39)( 7,44)( 8,43)( 9,45)
(10,50)(11,49)(12,51)(13,47)(14,46)(15,48)(16,53)(17,52)(18,54)(19,59)(20,58)
(21,60)(22,56)(23,55)(24,57)(25,62)(26,61)(27,63)(28,68)(29,67)(30,69)(31,65)
(32,64)(33,66)(34,71)(35,70)(36,72);
s2 := Sym(72)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27)
(31,34)(32,35)(33,36)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)(43,58)(44,59)
(45,60)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)(54,69);
poly := sub<Sym(72)|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*s2*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope