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# Polytope of Type {2,12,6}

Atlas Canonical Name : {2,12,6}*864e
if this polytope has a name.
Group : SmallGroup(864,4007)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 36, 108, 18
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,6,2} of size 1728
Vertex Figure Of :
{2,2,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,12,6}*432b
3-fold quotients : {2,4,6}*288
6-fold quotients : {2,4,6}*144
27-fold quotients : {2,4,2}*32
54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,24,6}*1728d, {4,12,6}*1728h, {2,12,12}*1728d
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)
(19,29)(20,28)(31,32)(34,35)(37,38)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)
(45,54)(46,56)(47,55);;
s2 := ( 3, 4)( 6,13)( 7,12)( 8,14)( 9,22)(10,21)(11,23)(15,17)(18,24)(19,26)
(20,25)(27,29)(30,31)(33,40)(34,39)(35,41)(36,49)(37,48)(38,50)(42,44)(45,51)
(46,53)(47,52)(54,56);;
s3 := ( 3,33)( 4,34)( 5,35)( 6,30)( 7,31)( 8,32)( 9,36)(10,37)(11,38)(12,51)
(13,52)(14,53)(15,48)(16,49)(17,50)(18,54)(19,55)(20,56)(21,42)(22,43)(23,44)
(24,39)(25,40)(26,41)(27,45)(28,46)(29,47);;
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope