Polytope of Type {6,42}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,42}*1512a
if this polytope has a name.
Group : SmallGroup(1512,486)
Rank : 3
Schlafli Type : {6,42}
Number of vertices, edges, etc : 18, 378, 126
Order of s₀s₁s₂ : 42
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) :
   3-fold quotients : {6,42}*504a
   7-fold quotients : {6,6}*216c
   9-fold quotients : {6,14}*168
   14-fold quotients : {3,6}*108
   21-fold quotients : {6,6}*72c
   27-fold quotients : {2,14}*56
   42-fold quotients : {3,6}*36
   54-fold quotients : {2,7}*28
   63-fold quotients : {6,2}*24
   126-fold quotients : {3,2}*12
   189-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      42 facets:
         42 of {6}*12
      10 vertex figures:
         4 of {42}*84
         6 of {14}*28

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,42}

Twisty Puzzle