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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6,21}*1512
if this polytope has a name.
Group : SmallGroup(1512,561)
Rank : 5
Schlafli Type : {2,3,6,21}
Number of vertices, edges, etc : 2, 3, 9, 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 : {2,3,2,21}*504
   7-fold quotients : {2,3,6,3}*216
   9-fold quotients : {2,3,2,7}*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)( 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);;
s2 := ( 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);;
s3 := ( 3,24)( 4,26)( 5,25)( 6,42)( 7,44)( 8,43)( 9,39)(10,41)(11,40)(12,36)
(13,38)(14,37)(15,33)(16,35)(17,34)(18,30)(19,32)(20,31)(21,27)(22,29)(23,28)
(46,47)(48,63)(49,65)(50,64)(51,60)(52,62)(53,61)(54,57)(55,59)(56,58);;
s4 := ( 3, 6)( 4, 8)( 5, 7)( 9,21)(10,23)(11,22)(12,18)(13,20)(14,19)(16,17)
(24,48)(25,50)(26,49)(27,45)(28,47)(29,46)(30,63)(31,65)(32,64)(33,60)(34,62)
(35,61)(36,57)(37,59)(38,58)(39,54)(40,56)(41,55)(42,51)(43,53)(44,52);;
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, 
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*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(65)!(1,2);
s1 := 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);
s2 := 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);
s3 := Sym(65)!( 3,24)( 4,26)( 5,25)( 6,42)( 7,44)( 8,43)( 9,39)(10,41)(11,40)
(12,36)(13,38)(14,37)(15,33)(16,35)(17,34)(18,30)(19,32)(20,31)(21,27)(22,29)
(23,28)(46,47)(48,63)(49,65)(50,64)(51,60)(52,62)(53,61)(54,57)(55,59)(56,58);
s4 := Sym(65)!( 3, 6)( 4, 8)( 5, 7)( 9,21)(10,23)(11,22)(12,18)(13,20)(14,19)
(16,17)(24,48)(25,50)(26,49)(27,45)(28,47)(29,46)(30,63)(31,65)(32,64)(33,60)
(34,62)(35,61)(36,57)(37,59)(38,58)(39,54)(40,56)(41,55)(42,51)(43,53)(44,52);
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, s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*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 >;

to this polytope