Polytope of Type {6,2,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,21}*504
if this polytope has a name.
Group : SmallGroup(504,192)
Rank : 4
Schlafli Type : {6,2,21}
Number of vertices, edges, etc : 6, 6, 21, 21
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,21,2} of size 1008
Vertex Figure Of :
   {2,6,2,21} of size 1008
   {3,6,2,21} of size 1512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,21}*252
   3-fold quotients : {6,2,7}*168, {2,2,21}*168
   6-fold quotients : {3,2,7}*84
   7-fold quotients : {6,2,3}*72
   9-fold quotients : {2,2,7}*56
   14-fold quotients : {3,2,3}*36
   21-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,21}*1008, {6,2,42}*1008
   3-fold covers : {6,2,63}*1512, {18,2,21}*1512, {6,6,21}*1512a, {6,6,21}*1512b
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s3 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(27)!(3,4)(5,6);
s1 := Sym(27)!(1,5)(2,3)(4,6);
s2 := Sym(27)!( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)
(26,27);
s3 := Sym(27)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26);
poly := sub<Sym(27)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

to this polytope