Polytope of Type {42,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,6}*1512a
if this polytope has a name.
Group : SmallGroup(1512,486)
Rank : 3
Schlafli Type : {42,6}
Number of vertices, edges, etc : 126, 378, 18
Order of s₀s₁s₂ : 42
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {42,6}*504a
   7-fold quotients : {6,6}*216a
   9-fold quotients : {14,6}*168
   14-fold quotients : {6,3}*108
   21-fold quotients : {6,6}*72b
   27-fold quotients : {14,2}*56
   42-fold quotients : {6,3}*36
   54-fold quotients : {7,2}*28
   63-fold quotients : {2,6}*24
   126-fold quotients : {2,3}*12
   189-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope