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Polytope of Type {44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44}*88
Also Known As : 44-gon, {44}. if this polytope has another name.
Group : SmallGroup(88,5)
Rank : 2
Schlafli Type : {44}
Number of vertices, edges, etc : 44, 44
Order of s0s1 : 44
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {44,2} of size 176
   {44,4} of size 352
   {44,6} of size 528
   {44,6} of size 528
   {44,4} of size 704
   {44,8} of size 704
   {44,8} of size 704
   {44,6} of size 792
   {44,10} of size 880
   {44,12} of size 1056
   {44,6} of size 1056
   {44,14} of size 1232
   {44,8} of size 1408
   {44,16} of size 1408
   {44,16} of size 1408
   {44,4} of size 1408
   {44,8} of size 1408
   {44,18} of size 1584
   {44,18} of size 1584
   {44,4} of size 1584
   {44,6} of size 1584
   {44,20} of size 1760
   {44,22} of size 1936
   {44,22} of size 1936
   {44,22} of size 1936
Vertex Figure Of :
   {2,44} of size 176
   {4,44} of size 352
   {6,44} of size 528
   {6,44} of size 528
   {4,44} of size 704
   {8,44} of size 704
   {8,44} of size 704
   {6,44} of size 792
   {10,44} of size 880
   {12,44} of size 1056
   {6,44} of size 1056
   {14,44} of size 1232
   {8,44} of size 1408
   {16,44} of size 1408
   {16,44} of size 1408
   {4,44} of size 1408
   {8,44} of size 1408
   {18,44} of size 1584
   {18,44} of size 1584
   {4,44} of size 1584
   {6,44} of size 1584
   {20,44} of size 1760
   {22,44} of size 1936
   {22,44} of size 1936
   {22,44} of size 1936
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22}*44
   4-fold quotients : {11}*22
   11-fold quotients : {4}*8
   22-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {88}*176
   3-fold covers : {132}*264
   4-fold covers : {176}*352
   5-fold covers : {220}*440
   6-fold covers : {264}*528
   7-fold covers : {308}*616
   8-fold covers : {352}*704
   9-fold covers : {396}*792
   10-fold covers : {440}*880
   11-fold covers : {484}*968
   12-fold covers : {528}*1056
   13-fold covers : {572}*1144
   14-fold covers : {616}*1232
   15-fold covers : {660}*1320
   16-fold covers : {704}*1408
   17-fold covers : {748}*1496
   18-fold covers : {792}*1584
   19-fold covers : {836}*1672
   20-fold covers : {880}*1760
   21-fold covers : {924}*1848
   22-fold covers : {968}*1936
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)
(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)
(43,44);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)(16,19)
(18,29)(20,31)(22,25)(24,27)(26,37)(28,39)(30,33)(32,35)(34,43)(36,40)(38,41)
(42,44);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(44)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)
(21,22)(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)
(43,44);
s1 := Sym(44)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)
(16,19)(18,29)(20,31)(22,25)(24,27)(26,37)(28,39)(30,33)(32,35)(34,43)(36,40)
(38,41)(42,44);
poly := sub<Sym(44)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*s0*s1 >; 
 
References : None.
to this polytope