Polytope of Type {2,44}

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

Permutation Representation (Magma) :

s0 := Sym(46)!(1,2);
s1 := Sym(46)!( 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(46)!( 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);
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*s1*s0*s1, s0*s2*s0*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*s1*s2 >;

to this polytope