Polytope of Type {2,22,2}

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

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,24);;
s3 := (25,26);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope