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# Polytope of Type {42,2,7}

Atlas Canonical Name : {42,2,7}*1176
if this polytope has a name.
Group : SmallGroup(1176,265)
Rank : 4
Schlafli Type : {42,2,7}
Number of vertices, edges, etc : 42, 42, 7, 7
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
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) :
2-fold quotients : {21,2,7}*588
3-fold quotients : {14,2,7}*392
6-fold quotients : {7,2,7}*196
7-fold quotients : {6,2,7}*168
14-fold quotients : {3,2,7}*84
21-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,22)
(23,26)(24,25)(27,28)(29,32)(30,31)(33,34)(35,38)(36,37)(39,42)(40,41);;
s1 := ( 1,17)( 2,11)( 3, 9)( 4,19)( 5, 7)( 6,29)( 8,13)(10,23)(12,21)(14,31)
(15,18)(16,39)(20,25)(22,35)(24,33)(26,41)(27,30)(28,40)(32,37)(34,36)
(38,42);;
s2 := (44,45)(46,47)(48,49);;
s3 := (43,44)(45,46)(47,48);;
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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope