Polytope of Type {22,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,2,3}*264
if this polytope has a name.
Group : SmallGroup(264,34)
Rank : 4
Schlafli Type : {22,2,3}
Number of vertices, edges, etc : 22, 22, 3, 3
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,2,3,2} of size 528
   {22,2,3,3} of size 1056
   {22,2,3,4} of size 1056
   {22,2,3,6} of size 1584
Vertex Figure Of :
   {2,22,2,3} of size 528
   {4,22,2,3} of size 1056
   {6,22,2,3} of size 1584
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {11,2,3}*132
   11-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,2,3}*528, {22,2,6}*528
   3-fold covers : {22,2,9}*792, {22,6,3}*792, {66,2,3}*792
   4-fold covers : {88,2,3}*1056, {22,2,12}*1056, {44,2,6}*1056, {22,4,6}*1056, {22,4,3}*1056
   5-fold covers : {22,2,15}*1320, {110,2,3}*1320
   6-fold covers : {44,2,9}*1584, {22,2,18}*1584, {44,6,3}*1584, {132,2,3}*1584, {22,6,6}*1584a, {22,6,6}*1584b, {66,2,6}*1584
   7-fold covers : {22,2,21}*1848, {154,2,3}*1848
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope