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Polytope of Type {42,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,6}*756
if this polytope has a name.
Group : SmallGroup(756,98)
Rank : 3
Schlafli Type : {42,6}
Number of vertices, edges, etc : 63, 189, 9
Order of s0s1s2 : 21
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {42,6,2} of size 1512
Vertex Figure Of :
   {2,42,6} of size 1512
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {6,6}*108
Covers (Minimal Covers in Boldface) :
   2-fold covers : {42,6}*1512c
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4,19)( 5,21)( 6,20)( 7,16)( 8,18)( 9,17)(10,13)(11,15)(12,14)
(22,43)(23,45)(24,44)(25,61)(26,63)(27,62)(28,58)(29,60)(30,59)(31,55)(32,57)
(33,56)(34,52)(35,54)(36,53)(37,49)(38,51)(39,50)(40,46)(41,48)(42,47);;
s1 := ( 1,25)( 2,26)( 3,27)( 4,22)( 5,23)( 6,24)( 7,40)( 8,41)( 9,42)(10,37)
(11,38)(12,39)(13,34)(14,35)(15,36)(16,31)(17,32)(18,33)(19,28)(20,29)(21,30)
(43,46)(44,47)(45,48)(49,61)(50,62)(51,63)(52,58)(53,59)(54,60);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,45)(46,48)(49,51)(52,54)(55,57)(58,60)
(61,63);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(63)!( 2, 3)( 4,19)( 5,21)( 6,20)( 7,16)( 8,18)( 9,17)(10,13)(11,15)
(12,14)(22,43)(23,45)(24,44)(25,61)(26,63)(27,62)(28,58)(29,60)(30,59)(31,55)
(32,57)(33,56)(34,52)(35,54)(36,53)(37,49)(38,51)(39,50)(40,46)(41,48)(42,47);
s1 := Sym(63)!( 1,25)( 2,26)( 3,27)( 4,22)( 5,23)( 6,24)( 7,40)( 8,41)( 9,42)
(10,37)(11,38)(12,39)(13,34)(14,35)(15,36)(16,31)(17,32)(18,33)(19,28)(20,29)
(21,30)(43,46)(44,47)(45,48)(49,61)(50,62)(51,63)(52,58)(53,59)(54,60);
s2 := Sym(63)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,23)(25,26)
(28,29)(31,32)(34,35)(37,38)(40,41)(43,45)(46,48)(49,51)(52,54)(55,57)(58,60)
(61,63);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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