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# Polytope of Type {2,2,36,6}

Atlas Canonical Name : {2,2,36,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,46114)
Rank : 5
Schlafli Type : {2,2,36,6}
Number of vertices, edges, etc : 2, 2, 36, 108, 6
Order of s0s1s2s3s4 : 18
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 : {2,2,12,6}*576d
9-fold quotients : {2,2,4,6}*192b
18-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14)(17,35)(18,36)(19,33)(20,34)
(21,31)(22,32)(23,29)(24,30)(25,39)(26,40)(27,37)(28,38);;
s3 := ( 5,17)( 6,19)( 7,18)( 8,20)( 9,25)(10,27)(11,26)(12,28)(13,21)(14,23)
(15,22)(16,24)(29,33)(30,35)(31,34)(32,36)(38,39);;
s4 := ( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40);;
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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14)(17,35)(18,36)(19,33)
(20,34)(21,31)(22,32)(23,29)(24,30)(25,39)(26,40)(27,37)(28,38);
s3 := Sym(40)!( 5,17)( 6,19)( 7,18)( 8,20)( 9,25)(10,27)(11,26)(12,28)(13,21)
(14,23)(15,22)(16,24)(29,33)(30,35)(31,34)(32,36)(38,39);
s4 := Sym(40)!( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40);
poly := sub<Sym(40)|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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4 >;

```

to this polytope