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# Polytope of Type {6,12}

Atlas Canonical Name : {6,12}*144c
if this polytope has a name.
Group : SmallGroup(144,154)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 6, 36, 12
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,12,2} of size 288
{6,12,4} of size 576
{6,12,6} of size 864
{6,12,3} of size 864
{6,12,6} of size 864
{6,12,8} of size 1152
{6,12,8} of size 1152
{6,12,4} of size 1152
{6,12,6} of size 1296
{6,12,10} of size 1440
{6,12,12} of size 1728
{6,12,12} of size 1728
{6,12,6} of size 1728
{6,12,4} of size 1728
{6,12,6} of size 1728
Vertex Figure Of :
{2,6,12} of size 288
{4,6,12} of size 576
{4,6,12} of size 576
{6,6,12} of size 864
{6,6,12} of size 864
{8,6,12} of size 1152
{4,6,12} of size 1152
{10,6,12} of size 1440
{12,6,12} of size 1728
{12,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,6}*72c
3-fold quotients : {6,4}*48a
4-fold quotients : {3,6}*36
6-fold quotients : {6,2}*24
9-fold quotients : {2,4}*16
12-fold quotients : {3,2}*12
18-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,12}*288c, {6,24}*288c
3-fold covers : {18,12}*432b, {6,12}*432c, {6,12}*432g
4-fold covers : {12,24}*576a, {12,12}*576c, {12,24}*576b, {24,12}*576d, {24,12}*576f, {6,48}*576c, {6,12}*576e, {6,12}*576f
5-fold covers : {6,60}*720a, {30,12}*720c
6-fold covers : {36,12}*864b, {12,12}*864a, {18,24}*864b, {6,24}*864c, {6,24}*864f, {12,12}*864h
7-fold covers : {6,84}*1008a, {42,12}*1008c
8-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, {6,96}*1152a, {12,12}*1152l, {12,12}*1152m, {6,24}*1152j, {6,24}*1152k, {6,12}*1152e, {6,24}*1152l, {12,12}*1152q, {12,12}*1152s, {6,12}*1152f, {6,24}*1152m
9-fold covers : {18,36}*1296c, {18,12}*1296e, {54,12}*1296b, {18,12}*1296f, {18,12}*1296g, {18,12}*1296h, {6,12}*1296d, {6,36}*1296h, {6,36}*1296l, {18,12}*1296l, {6,12}*1296g, {6,12}*1296h, {6,12}*1296i, {6,12}*1296s
10-fold covers : {6,120}*1440a, {12,60}*1440a, {60,12}*1440c, {30,24}*1440c
11-fold covers : {6,132}*1584a, {66,12}*1584c
12-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, {18,48}*1728b, {6,48}*1728c, {6,48}*1728f, {12,24}*1728o, {24,12}*1728o, {12,24}*1728p, {24,12}*1728p, {12,12}*1728h, {18,12}*1728b, {18,12}*1728d, {6,12}*1728e, {6,12}*1728f, {12,12}*1728w, {6,12}*1728h, {6,12}*1728i
13-fold covers : {6,156}*1872a, {78,12}*1872c
Permutation Representation (GAP) :
```s0 := ( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)
(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,55)(20,57)(21,56)
(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)
(33,71)(34,67)(35,69)(36,68);;
s1 := ( 1,59)( 2,58)( 3,60)( 4,56)( 5,55)( 6,57)( 7,62)( 8,61)( 9,63)(10,68)
(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,41)(20,40)(21,42)
(22,38)(23,37)(24,39)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)(32,46)
(33,48)(34,53)(35,52)(36,54);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(19,28)(20,30)(21,29)(22,31)
(23,33)(24,32)(25,34)(26,36)(27,35)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)
(55,64)(56,66)(57,65)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71);;
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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope