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# Polytope of Type {12,12}

Atlas Canonical Name : {12,12}*288b
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
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,12,2} of size 576
{12,12,4} of size 1152
{12,12,4} of size 1152
{12,12,4} of size 1152
{12,12,6} of size 1728
{12,12,6} of size 1728
Vertex Figure Of :
{2,12,12} of size 576
{4,12,12} of size 1152
{6,12,12} of size 1728
{3,12,12} of size 1728
{6,12,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,12}*144b, {12,6}*144c
3-fold quotients : {4,12}*96a
4-fold quotients : {6,6}*72b
6-fold quotients : {2,12}*48, {4,6}*48a
8-fold quotients : {6,3}*36
9-fold quotients : {4,4}*32
12-fold quotients : {2,6}*24
18-fold quotients : {2,4}*16, {4,2}*16
24-fold quotients : {2,3}*12
36-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,12}*576a, {12,12}*576b, {24,12}*576b, {12,24}*576d, {12,24}*576f
3-fold covers : {12,36}*864b, {12,12}*864b, {12,12}*864h
4-fold covers : {12,24}*1152a, {24,12}*1152c, {24,24}*1152a, {24,24}*1152f, {24,24}*1152h, {24,24}*1152j, {12,48}*1152a, {48,12}*1152c, {12,48}*1152d, {48,12}*1152f, {12,12}*1152b, {24,12}*1152d, {12,24}*1152f, {12,12}*1152j, {12,12}*1152o
5-fold covers : {60,12}*1440a, {12,60}*1440c
6-fold covers : {24,36}*1728a, {24,12}*1728a, {12,36}*1728b, {12,12}*1728b, {24,36}*1728b, {24,12}*1728b, {12,72}*1728b, {12,24}*1728c, {12,72}*1728d, {12,24}*1728e, {12,24}*1728o, {24,12}*1728o, {12,24}*1728p, {24,12}*1728p, {12,12}*1728h
Permutation Representation (GAP) :
```s0 := ( 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);;
s1 := ( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)(10,49)
(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,58)(20,60)(21,59)
(22,55)(23,57)(24,56)(25,61)(26,63)(27,62)(28,67)(29,69)(30,68)(31,64)(32,66)
(33,65)(34,70)(35,72)(36,71);;
s2 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)(22,26)
(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,65)(38,64)(39,66)(40,71)(41,70)
(42,72)(43,68)(44,67)(45,69)(46,56)(47,55)(48,57)(49,62)(50,61)(51,63)(52,59)
(53,58)(54,60);;
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*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,
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(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);
s1 := Sym(72)!( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)
(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,58)(20,60)
(21,59)(22,55)(23,57)(24,56)(25,61)(26,63)(27,62)(28,67)(29,69)(30,68)(31,64)
(32,66)(33,65)(34,70)(35,72)(36,71);
s2 := Sym(72)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)
(22,26)(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,65)(38,64)(39,66)(40,71)
(41,70)(42,72)(43,68)(44,67)(45,69)(46,56)(47,55)(48,57)(49,62)(50,61)(51,63)
(52,59)(53,58)(54,60);
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*s0*s1*s2*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,
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