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# Polytope of Type {2,6,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,12}*1728h
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 5
Schlafli Type : {2,6,6,12}
Number of vertices, edges, etc : 2, 6, 18, 36, 12
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,2,6,12}*576d, {2,6,6,4}*576f
6-fold quotients : {2,6,3,4}*288
9-fold quotients : {2,2,6,4}*192b
18-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)(32,36)
(33,37)(34,38);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,19)(16,21)(17,20)(18,22)(24,25)
(27,31)(28,33)(29,32)(30,34)(36,37);;
s3 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(15,27)(16,28)(17,30)(18,29)(19,35)
(20,36)(21,38)(22,37)(23,31)(24,32)(25,34)(26,33);;
s4 := ( 3,18)( 4,17)( 5,16)( 6,15)( 7,22)( 8,21)( 9,20)(10,19)(11,26)(12,25)
(13,24)(14,23)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s2*s3*s4*s2*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)
(32,36)(33,37)(34,38);
s2 := Sym(38)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,19)(16,21)(17,20)(18,22)
(24,25)(27,31)(28,33)(29,32)(30,34)(36,37);
s3 := Sym(38)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(15,27)(16,28)(17,30)(18,29)
(19,35)(20,36)(21,38)(22,37)(23,31)(24,32)(25,34)(26,33);
s4 := Sym(38)!( 3,18)( 4,17)( 5,16)( 6,15)( 7,22)( 8,21)( 9,20)(10,19)(11,26)
(12,25)(13,24)(14,23)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37);
poly := sub<Sym(38)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s2*s3*s4*s2*s3*s4,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 >;

```

to this polytope