Polytope of Type {2,2,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,44}*352
if this polytope has a name.
Group : SmallGroup(352,175)
Rank : 4
Schlafli Type : {2,2,44}
Number of vertices, edges, etc : 2, 2, 44, 44
Order of s₀s₁s₂s₃ : 44
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,44,2} of size 704
   {2,2,44,4} of size 1408
Vertex Figure Of :
   {2,2,2,44} of size 704
   {3,2,2,44} of size 1056
   {4,2,2,44} of size 1408
   {5,2,2,44} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,22}*176
   4-fold quotients : {2,2,11}*88
   11-fold quotients : {2,2,4}*32
   22-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,44}*704, {4,2,44}*704, {2,2,88}*704
   3-fold covers : {2,6,44}*1056a, {6,2,44}*1056, {2,2,132}*1056
   4-fold covers : {4,4,44}*1408, {2,8,44}*1408a, {2,4,88}*1408a, {2,8,44}*1408b, {2,4,88}*1408b, {2,4,44}*1408, {8,2,44}*1408, {4,2,88}*1408, {2,2,176}*1408
   5-fold covers : {2,10,44}*1760, {10,2,44}*1760, {2,2,220}*1760
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)(25,26)
(27,30)(28,29)(31,32)(33,34)(35,38)(36,37)(39,40)(41,42)(43,46)(44,45)
(47,48);;
s3 := ( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)(20,23)
(22,33)(24,35)(26,29)(28,31)(30,41)(32,43)(34,37)(36,39)(38,47)(40,44)(42,45)
(46,48);;
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*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(48)!(1,2);
s1 := Sym(48)!(3,4);
s2 := Sym(48)!( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)
(25,26)(27,30)(28,29)(31,32)(33,34)(35,38)(36,37)(39,40)(41,42)(43,46)(44,45)
(47,48);
s3 := Sym(48)!( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)
(20,23)(22,33)(24,35)(26,29)(28,31)(30,41)(32,43)(34,37)(36,39)(38,47)(40,44)
(42,45)(46,48);
poly := sub<Sym(48)|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*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 >;

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