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# Polytope of Type {4,42}

Atlas Canonical Name : {4,42}*1008
if this polytope has a name.
Group : SmallGroup(1008,896)
Rank : 3
Schlafli Type : {4,42}
Number of vertices, edges, etc : 12, 252, 126
Order of s0s1s2 : 28
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {4,6}*144
9-fold quotients : {4,14}*112
14-fold quotients : {4,6}*72
18-fold quotients : {2,14}*56
36-fold quotients : {2,7}*28
63-fold quotients : {4,2}*16
126-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 8,22)( 9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(15,43)(16,44)(17,45)
(18,46)(19,47)(20,48)(21,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)
(42,56);;
s1 := ( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(22,43)
(23,49)(24,48)(25,47)(26,46)(27,45)(28,44)(29,50)(30,56)(31,55)(32,54)(33,53)
(34,52)(35,51)(36,57)(37,63)(38,62)(39,61)(40,60)(41,59)(42,58);;
s2 := ( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,23)( 9,22)(10,28)
(11,27)(12,26)(13,25)(14,24)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)
(43,51)(44,50)(45,56)(46,55)(47,54)(48,53)(49,52)(57,58)(59,63)(60,62);;
poly := Group([s0,s1,s2]);;

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

```
Permutation Representation (Magma) :
```s0 := Sym(63)!( 8,22)( 9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(15,43)(16,44)
(17,45)(18,46)(19,47)(20,48)(21,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)
(42,56);
s1 := Sym(63)!( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)
(22,43)(23,49)(24,48)(25,47)(26,46)(27,45)(28,44)(29,50)(30,56)(31,55)(32,54)
(33,53)(34,52)(35,51)(36,57)(37,63)(38,62)(39,61)(40,60)(41,59)(42,58);
s2 := Sym(63)!( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,23)( 9,22)
(10,28)(11,27)(12,26)(13,25)(14,24)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)
(21,38)(43,51)(44,50)(45,56)(46,55)(47,54)(48,53)(49,52)(57,58)(59,63)(60,62);
poly := sub<Sym(63)|s0,s1,s2>;

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

```
References : None.
to this polytope