Polytope of Type {22,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,2,2}*176
if this polytope has a name.
Group : SmallGroup(176,41)
Rank : 4
Schlafli Type : {22,2,2}
Number of vertices, edges, etc : 22, 22, 2, 2
Order of s₀s₁s₂s₃ : 22
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,2,2,2} of size 352
   {22,2,2,3} of size 528
   {22,2,2,4} of size 704
   {22,2,2,5} of size 880
   {22,2,2,6} of size 1056
   {22,2,2,7} of size 1232
   {22,2,2,8} of size 1408
   {22,2,2,9} of size 1584
   {22,2,2,10} of size 1760
   {22,2,2,11} of size 1936
Vertex Figure Of :
   {2,22,2,2} of size 352
   {4,22,2,2} of size 704
   {6,22,2,2} of size 1056
   {8,22,2,2} of size 1408
   {10,22,2,2} of size 1760
   {11,22,2,2} of size 1936
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {11,2,2}*88
   11-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,2,2}*352, {22,2,4}*352, {22,4,2}*352
   3-fold covers : {22,2,6}*528, {22,6,2}*528, {66,2,2}*528
   4-fold covers : {44,4,2}*704, {44,2,4}*704, {22,4,4}*704, {88,2,2}*704, {22,2,8}*704, {22,8,2}*704
   5-fold covers : {22,2,10}*880, {22,10,2}*880, {110,2,2}*880
   6-fold covers : {22,2,12}*1056, {22,12,2}*1056, {44,2,6}*1056, {44,6,2}*1056a, {22,4,6}*1056, {22,6,4}*1056a, {132,2,2}*1056, {66,2,4}*1056, {66,4,2}*1056a
   7-fold covers : {22,2,14}*1232, {22,14,2}*1232, {154,2,2}*1232
   8-fold covers : {44,4,4}*1408, {22,4,8}*1408a, {22,8,4}*1408a, {44,8,2}*1408a, {88,4,2}*1408a, {22,4,8}*1408b, {22,8,4}*1408b, {44,8,2}*1408b, {88,4,2}*1408b, {22,4,4}*1408, {44,4,2}*1408, {44,2,8}*1408, {88,2,4}*1408, {22,2,16}*1408, {22,16,2}*1408, {176,2,2}*1408
   9-fold covers : {22,2,18}*1584, {22,18,2}*1584, {198,2,2}*1584, {22,6,6}*1584a, {22,6,6}*1584b, {22,6,6}*1584c, {66,6,2}*1584a, {66,2,6}*1584, {66,6,2}*1584b, {66,6,2}*1584c
   10-fold covers : {22,2,20}*1760, {22,20,2}*1760, {44,2,10}*1760, {44,10,2}*1760, {22,4,10}*1760, {22,10,4}*1760, {220,2,2}*1760, {110,2,4}*1760, {110,4,2}*1760
   11-fold covers : {242,2,2}*1936, {22,2,22}*1936, {22,22,2}*1936a, {22,22,2}*1936c
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 := (23,24);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*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(26)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22);
s1 := Sym(26)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,22);
s2 := Sym(26)!(23,24);
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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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