Polytope of Type {44,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,2}*176
if this polytope has a name.
Group : SmallGroup(176,29)
Rank : 3
Schlafli Type : {44,2}
Number of vertices, edges, etc : 44, 44, 2
Order of s₀s₁s₂ : 44
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {44,2,2} of size 352
   {44,2,3} of size 528
   {44,2,4} of size 704
   {44,2,5} of size 880
   {44,2,6} of size 1056
   {44,2,7} of size 1232
   {44,2,8} of size 1408
   {44,2,9} of size 1584
   {44,2,10} of size 1760
   {44,2,11} of size 1936
Vertex Figure Of :
   {2,44,2} of size 352
   {4,44,2} of size 704
   {6,44,2} of size 1056
   {6,44,2} of size 1056
   {8,44,2} of size 1408
   {8,44,2} of size 1408
   {4,44,2} of size 1408
   {6,44,2} of size 1584
   {10,44,2} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22,2}*88
   4-fold quotients : {11,2}*44
   11-fold quotients : {4,2}*16
   22-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,4}*352, {88,2}*352
   3-fold covers : {44,6}*528a, {132,2}*528
   4-fold covers : {88,4}*704a, {44,4}*704, {88,4}*704b, {44,8}*704a, {44,8}*704b, {176,2}*704
   5-fold covers : {44,10}*880, {220,2}*880
   6-fold covers : {88,6}*1056, {44,12}*1056, {132,4}*1056a, {264,2}*1056
   7-fold covers : {44,14}*1232, {308,2}*1232
   8-fold covers : {44,8}*1408a, {88,4}*1408a, {88,8}*1408a, {88,8}*1408b, {88,8}*1408c, {88,8}*1408d, {44,16}*1408a, {176,4}*1408a, {44,16}*1408b, {176,4}*1408b, {44,4}*1408, {88,4}*1408b, {44,8}*1408b, {352,2}*1408
   9-fold covers : {44,18}*1584a, {396,2}*1584, {132,6}*1584a, {132,6}*1584b, {132,6}*1584c, {44,6}*1584
   10-fold covers : {88,10}*1760, {44,20}*1760, {220,4}*1760, {440,2}*1760
   11-fold covers : {484,2}*1936, {44,22}*1936a, {44,22}*1936b
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);;
s2 := (45,46);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
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(46)!( 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(46)!( 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);
s2 := Sym(46)!(45,46);
poly := sub<Sym(46)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, 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 >;

to this polytope