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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,21,6,3}*1512
if this polytope has a name.
Group : SmallGroup(1512,561)
Rank : 5
Schlafli Type : {2,21,6,3}
Number of vertices, edges, etc : 2, 21, 63, 9, 3
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 : {2,21,2,3}*504
   7-fold quotients : {2,3,6,3}*216
   9-fold quotients : {2,7,2,3}*168
   21-fold quotients : {2,3,2,3}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope