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# Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*864d
if this polytope has a name.
Group : SmallGroup(864,4000)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 36, 108, 18
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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) :
3-fold quotients : {2,12,6}*288d
4-fold quotients : {2,6,6}*216
9-fold quotients : {2,4,6}*96b
18-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,6}*1728b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,29)(16,30)(17,27)(18,28)
(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32);;
s2 := ( 3,15)( 4,17)( 5,16)( 6,18)( 7,19)( 8,21)( 9,20)(10,22)(11,23)(12,25)
(13,24)(14,26)(28,29)(32,33)(36,37);;
s3 := ( 4, 6)( 7,11)( 8,14)( 9,13)(10,12)(15,23)(16,26)(17,25)(18,24)(20,22)
(27,31)(28,34)(29,33)(30,32)(36,38);;
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,
s1*s2*s3*s1*s2*s3*s1*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(38)!(1,2);
s1 := Sym(38)!( 3, 5)( 4, 6)( 7,13)( 8,14)( 9,11)(10,12)(15,29)(16,30)(17,27)
(18,28)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32);
s2 := Sym(38)!( 3,15)( 4,17)( 5,16)( 6,18)( 7,19)( 8,21)( 9,20)(10,22)(11,23)
(12,25)(13,24)(14,26)(28,29)(32,33)(36,37);
s3 := Sym(38)!( 4, 6)( 7,11)( 8,14)( 9,13)(10,12)(15,23)(16,26)(17,25)(18,24)
(20,22)(27,31)(28,34)(29,33)(30,32)(36,38);
poly := sub<Sym(38)|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, s1*s2*s3*s1*s2*s3*s1*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope