Polytope of Type {3,2,21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,21}*252
if this polytope has a name.
Group : SmallGroup(252,36)
Rank : 4
Schlafli Type : {3,2,21}
Number of vertices, edges, etc : 3, 3, 21, 21
Order of s₀s₁s₂s₃ : 21
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,21,2} of size 504
   {3,2,21,4} of size 1008
   {3,2,21,6} of size 1512
Vertex Figure Of :
   {2,3,2,21} of size 504
   {3,3,2,21} of size 1008
   {4,3,2,21} of size 1008
   {6,3,2,21} of size 1512
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,7}*84
   7-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,42}*504, {6,2,21}*504
   3-fold covers : {3,2,63}*756, {9,2,21}*756, {3,6,21}*756
   4-fold covers : {12,2,21}*1008, {3,2,84}*1008, {6,2,42}*1008
   5-fold covers : {15,2,21}*1260, {3,2,105}*1260
   6-fold covers : {3,2,126}*1512, {6,2,63}*1512, {9,2,42}*1512, {18,2,21}*1512, {3,6,42}*1512a, {6,6,21}*1512a, {3,6,42}*1512b, {6,6,21}*1512b
   7-fold covers : {3,2,147}*1764, {21,2,21}*1764
Permutation Representation (GAP) :

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