Polytope of Type {3,2,6,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,21}*1512
if this polytope has a name.
Group : SmallGroup(1512,838)
Rank : 5
Schlafli Type : {3,2,6,21}
Number of vertices, edges, etc : 3, 3, 6, 63, 21
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
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 : {3,2,2,21}*504
   7-fold quotients : {3,2,6,3}*216
   9-fold quotients : {3,2,2,7}*168
   21-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (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)(43,64)(44,65)
(45,66);;
s3 := ( 4,25)( 5,31)( 6,30)( 7,29)( 8,28)( 9,27)(10,26)(11,39)(12,45)(13,44)
(14,43)(15,42)(16,41)(17,40)(18,32)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)
(47,52)(48,51)(49,50)(53,60)(54,66)(55,65)(56,64)(57,63)(58,62)(59,61);;
s4 := ( 4,12)( 5,11)( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(18,19)(20,24)(21,23)
(25,54)(26,53)(27,59)(28,58)(29,57)(30,56)(31,55)(32,47)(33,46)(34,52)(35,51)
(36,50)(37,49)(38,48)(39,61)(40,60)(41,66)(42,65)(43,64)(44,63)(45,62);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!(2,3);
s1 := Sym(66)!(1,2);
s2 := Sym(66)!(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)(43,64)(44,65)
(45,66);
s3 := Sym(66)!( 4,25)( 5,31)( 6,30)( 7,29)( 8,28)( 9,27)(10,26)(11,39)(12,45)
(13,44)(14,43)(15,42)(16,41)(17,40)(18,32)(19,38)(20,37)(21,36)(22,35)(23,34)
(24,33)(47,52)(48,51)(49,50)(53,60)(54,66)(55,65)(56,64)(57,63)(58,62)(59,61);
s4 := Sym(66)!( 4,12)( 5,11)( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(18,19)(20,24)
(21,23)(25,54)(26,53)(27,59)(28,58)(29,57)(30,56)(31,55)(32,47)(33,46)(34,52)
(35,51)(36,50)(37,49)(38,48)(39,61)(40,60)(41,66)(42,65)(43,64)(44,63)(45,62);
poly := sub<Sym(66)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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