Polytope of Type {3,2,22}

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

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

Permutation Representation (Magma) :

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

to this polytope