Polytope of Type {21,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21,6}*756
if this polytope has a name.
Group : SmallGroup(756,98)
Rank : 3
Schlafli Type : {21,6}
Number of vertices, edges, etc : 63, 189, 18
Order of s0s1s2 : 42
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {21,6,2} of size 1512
Vertex Figure Of :
   {2,21,6} of size 1512
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {21,6}*252
   7-fold quotients : {3,6}*108
   9-fold quotients : {21,2}*84
   21-fold quotients : {3,6}*36
   27-fold quotients : {7,2}*28
   63-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {42,6}*1512b
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      6 facets:
         6 of {21}*42
      35 vertex figures:
         14 of {6}*12
         21 of {2}*4

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