Polytope of Type {42,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,4}*1008
if this polytope has a name.
Group : SmallGroup(1008,896)
Rank : 3
Schlafli Type : {42,4}
Number of vertices, edges, etc : 126, 252, 12
Order of s0s1s2 : 28
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {6,4}*144
   9-fold quotients : {14,4}*112
   14-fold quotients : {6,4}*72
   18-fold quotients : {14,2}*56
   36-fold quotients : {7,2}*28
   63-fold quotients : {2,4}*16
   126-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*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1> of order 2.
      7 facets:
         5 of {42}*84
         2 of {21}*42
      63 vertex figures:
         63 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      6 facets:
         6 of {42}*84
      63 vertex figures:
         63 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 3.
      8 facets:
         2 of {42}*84
         6 of {14}*28
      42 vertex figures:
         42 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      4 facets:
         4 of {42}*84
      42 vertex figures:
         42 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 6.
      5 facets:
         3 of {14}*28
         2 of {21}*42
      21 vertex figures:
         21 of {4}*8

Permutation Representation (GAP) : 
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(22,43)(23,49)(24,48)(25,47)(26,46)(27,45)(28,44)(29,57)(30,63)(31,62)(32,61)(33,60)(34,59)(35,58)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51);;
s1 := ( 1,23)( 2,22)( 3,28)( 4,27)( 5,26)( 6,25)( 7,24)( 8,30)( 9,29)(10,35)(11,34)(12,33)(13,32)(14,31)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(43,44)(45,49)(46,48)(50,51)(52,56)(53,55)(57,58)(59,63)(60,62);;
s2 := ( 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);;
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, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(63)!( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(22,43)(23,49)(24,48)(25,47)(26,46)(27,45)(28,44)(29,57)(30,63)(31,62)(32,61)(33,60)(34,59)(35,58)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51);
s1 := Sym(63)!( 1,23)( 2,22)( 3,28)( 4,27)( 5,26)( 6,25)( 7,24)( 8,30)( 9,29)(10,35)(11,34)(12,33)(13,32)(14,31)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(43,44)(45,49)(46,48)(50,51)(52,56)(53,55)(57,58)(59,63)(60,62);
s2 := 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);
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, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 >;
References : None.
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Twisty Puzzle