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Polytope of Type {2,44,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,44,2}*352
if this polytope has a name.
Group : SmallGroup(352,175)
Rank : 4
Schlafli Type : {2,44,2}
Number of vertices, edges, etc : 2, 44, 44, 2
Order of s0s1s2s3 : 44
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,44,2,2} of size 704
   {2,44,2,3} of size 1056
   {2,44,2,4} of size 1408
   {2,44,2,5} of size 1760
Vertex Figure Of :
   {2,2,44,2} of size 704
   {3,2,44,2} of size 1056
   {4,2,44,2} of size 1408
   {5,2,44,2} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,22,2}*176
   4-fold quotients : {2,11,2}*88
   11-fold quotients : {2,4,2}*32
   22-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,44,4}*704, {4,44,2}*704, {2,88,2}*704
   3-fold covers : {2,44,6}*1056a, {6,44,2}*1056a, {2,132,2}*1056
   4-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, {2,176,2}*1408
   5-fold covers : {2,44,10}*1760, {10,44,2}*1760, {2,220,2}*1760
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)(23,24)
(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38)(39,40)(41,44)(42,43)
(45,46);;
s2 := ( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)(18,21)
(20,31)(22,33)(24,27)(26,29)(28,39)(30,41)(32,35)(34,37)(36,45)(38,42)(40,43)
(44,46);;
s3 := (47,48);;
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, 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*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(48)!(1,2);
s1 := Sym(48)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22)
(23,24)(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38)(39,40)(41,44)(42,43)
(45,46);
s2 := Sym(48)!( 3, 9)( 4, 6)( 5,15)( 7,17)( 8,11)(10,13)(12,23)(14,25)(16,19)
(18,21)(20,31)(22,33)(24,27)(26,29)(28,39)(30,41)(32,35)(34,37)(36,45)(38,42)
(40,43)(44,46);
s3 := Sym(48)!(47,48);
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, 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*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 >; 
 

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