Polytope of Type {6,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,42}*756
if this polytope has a name.
Group : SmallGroup(756,98)
Rank : 3
Schlafli Type : {6,42}
Number of vertices, edges, etc : 9, 189, 63
Order of s₀s₁s₂ : 21
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,42,2} of size 1512
Vertex Figure Of :
   {2,6,42} of size 1512
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {6,6}*108
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,42}*1512c
Permutation Representation (GAP) :

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

References : None.
to this polytope