Polytope of Type {4,2,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,22}*352
if this polytope has a name.
Group : SmallGroup(352,177)
Rank : 4
Schlafli Type : {4,2,22}
Number of vertices, edges, etc : 4, 4, 22, 22
Order of s₀s₁s₂s₃ : 44
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,22,2} of size 704
   {4,2,22,4} of size 1408
Vertex Figure Of :
   {2,4,2,22} of size 704
   {3,4,2,22} of size 1056
   {4,4,2,22} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,11}*176, {2,2,22}*176
   4-fold quotients : {2,2,11}*88
   11-fold quotients : {4,2,2}*32
   22-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,44}*704, {4,4,22}*704, {8,2,22}*704
   3-fold covers : {12,2,22}*1056, {4,6,22}*1056a, {4,2,66}*1056
   4-fold covers : {4,4,44}*1408, {4,8,22}*1408a, {8,4,22}*1408a, {4,8,22}*1408b, {8,4,22}*1408b, {4,4,22}*1408, {8,2,44}*1408, {4,2,88}*1408, {16,2,22}*1408
   5-fold covers : {20,2,22}*1760, {4,10,22}*1760, {4,2,110}*1760
Permutation Representation (GAP) :

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