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# Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*288c
if this polytope has a name.
Group : SmallGroup(288,977)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 6, 36, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,12,2} of size 576
{2,6,12,4} of size 1152
{2,6,12,6} of size 1728
{2,6,12,3} of size 1728
{2,6,12,6} of size 1728
Vertex Figure Of :
{2,2,6,12} of size 576
{3,2,6,12} of size 864
{4,2,6,12} of size 1152
{5,2,6,12} of size 1440
{6,2,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,6}*144c
3-fold quotients : {2,6,4}*96a
4-fold quotients : {2,3,6}*72
6-fold quotients : {2,6,2}*48
9-fold quotients : {2,2,4}*32
12-fold quotients : {2,3,2}*24
18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,12}*576c, {2,6,24}*576c, {4,6,12}*576c
3-fold covers : {2,18,12}*864b, {2,6,12}*864c, {2,6,12}*864g, {6,6,12}*864f, {6,6,12}*864g
4-fold covers : {4,12,12}*1152a, {2,24,12}*1152b, {2,12,24}*1152c, {2,24,12}*1152e, {2,12,24}*1152f, {2,12,12}*1152c, {8,6,12}*1152a, {4,6,24}*1152a, {2,6,48}*1152a, {4,6,12}*1152d, {2,6,12}*1152e, {2,6,12}*1152f
5-fold covers : {2,6,60}*1440a, {10,6,12}*1440c, {2,30,12}*1440c
6-fold covers : {2,36,12}*1728b, {2,12,12}*1728a, {2,18,24}*1728b, {4,18,12}*1728b, {2,6,24}*1728c, {4,6,12}*1728c, {2,6,24}*1728f, {12,6,12}*1728d, {6,12,12}*1728e, {6,12,12}*1728f, {6,6,24}*1728f, {6,6,24}*1728g, {2,12,12}*1728h, {12,6,12}*1728g, {4,6,12}*1728h
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,48)
(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,57)(22,59)(23,58)
(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)(34,74)
(35,73)(36,69)(37,71)(38,70);;
s2 := ( 3,61)( 4,60)( 5,62)( 6,58)( 7,57)( 8,59)( 9,64)(10,63)(11,65)(12,70)
(13,69)(14,71)(15,67)(16,66)(17,68)(18,73)(19,72)(20,74)(21,43)(22,42)(23,44)
(24,40)(25,39)(26,41)(27,46)(28,45)(29,47)(30,52)(31,51)(32,53)(33,49)(34,48)
(35,50)(36,55)(37,54)(38,56);;
s3 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)(24,33)
(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)
(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)
(12,48)(13,50)(14,49)(15,54)(16,56)(17,55)(18,51)(19,53)(20,52)(21,57)(22,59)
(23,58)(24,63)(25,65)(26,64)(27,60)(28,62)(29,61)(30,66)(31,68)(32,67)(33,72)
(34,74)(35,73)(36,69)(37,71)(38,70);
s2 := Sym(74)!( 3,61)( 4,60)( 5,62)( 6,58)( 7,57)( 8,59)( 9,64)(10,63)(11,65)
(12,70)(13,69)(14,71)(15,67)(16,66)(17,68)(18,73)(19,72)(20,74)(21,43)(22,42)
(23,44)(24,40)(25,39)(26,41)(27,46)(28,45)(29,47)(30,52)(31,51)(32,53)(33,49)
(34,48)(35,50)(36,55)(37,54)(38,56);
s3 := Sym(74)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)
(24,33)(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)
(55,56)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);
poly := sub<Sym(74)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope