Polytope of Type {2,2,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,22}*176
if this polytope has a name.
Group : SmallGroup(176,41)
Rank : 4
Schlafli Type : {2,2,22}
Number of vertices, edges, etc : 2, 2, 22, 22
Order of s₀s₁s₂s₃ : 22
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,22,2} of size 352
   {2,2,22,4} of size 704
   {2,2,22,6} of size 1056
   {2,2,22,8} of size 1408
   {2,2,22,10} of size 1760
   {2,2,22,11} of size 1936
Vertex Figure Of :
   {2,2,2,22} of size 352
   {3,2,2,22} of size 528
   {4,2,2,22} of size 704
   {5,2,2,22} of size 880
   {6,2,2,22} of size 1056
   {7,2,2,22} of size 1232
   {8,2,2,22} of size 1408
   {9,2,2,22} of size 1584
   {10,2,2,22} of size 1760
   {11,2,2,22} of size 1936
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,11}*88
   11-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,44}*352, {2,4,22}*352, {4,2,22}*352
   3-fold covers : {2,6,22}*528, {6,2,22}*528, {2,2,66}*528
   4-fold covers : {2,4,44}*704, {4,2,44}*704, {4,4,22}*704, {2,2,88}*704, {2,8,22}*704, {8,2,22}*704
   5-fold covers : {2,10,22}*880, {10,2,22}*880, {2,2,110}*880
   6-fold covers : {2,12,22}*1056, {12,2,22}*1056, {2,6,44}*1056a, {6,2,44}*1056, {4,6,22}*1056a, {6,4,22}*1056, {2,2,132}*1056, {2,4,66}*1056a, {4,2,66}*1056
   7-fold covers : {2,14,22}*1232, {14,2,22}*1232, {2,2,154}*1232
   8-fold covers : {4,4,44}*1408, {4,8,22}*1408a, {8,4,22}*1408a, {2,8,44}*1408a, {2,4,88}*1408a, {4,8,22}*1408b, {8,4,22}*1408b, {2,8,44}*1408b, {2,4,88}*1408b, {4,4,22}*1408, {2,4,44}*1408, {8,2,44}*1408, {4,2,88}*1408, {2,16,22}*1408, {16,2,22}*1408, {2,2,176}*1408
   9-fold covers : {2,18,22}*1584, {18,2,22}*1584, {2,2,198}*1584, {6,6,22}*1584a, {6,6,22}*1584b, {6,6,22}*1584c, {2,6,66}*1584a, {2,6,66}*1584b, {2,6,66}*1584c, {6,2,66}*1584
   10-fold covers : {2,20,22}*1760, {20,2,22}*1760, {2,10,44}*1760, {10,2,44}*1760, {4,10,22}*1760, {10,4,22}*1760, {2,2,220}*1760, {2,4,110}*1760, {4,2,110}*1760
   11-fold covers : {2,2,242}*1936, {2,22,22}*1936a, {2,22,22}*1936b, {22,2,22}*1936
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!(1,2);
s1 := Sym(26)!(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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3 >;

to this polytope