Polytope of Type {2,37}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,37}*148
if this polytope has a name.
Group : SmallGroup(148,4)
Rank : 3
Schlafli Type : {2,37}
Number of vertices, edges, etc : 2, 37, 37
Order of s₀s₁s₂ : 74
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,37,2} of size 296
Vertex Figure Of :
   {2,2,37} of size 296
   {3,2,37} of size 444
   {4,2,37} of size 592
   {5,2,37} of size 740
   {6,2,37} of size 888
   {7,2,37} of size 1036
   {8,2,37} of size 1184
   {9,2,37} of size 1332
   {10,2,37} of size 1480
   {11,2,37} of size 1628
   {12,2,37} of size 1776
   {13,2,37} of size 1924
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,74}*296
   3-fold covers : {2,111}*444
   4-fold covers : {2,148}*592, {4,74}*592
   5-fold covers : {2,185}*740
   6-fold covers : {6,74}*888, {2,222}*888
   7-fold covers : {2,259}*1036
   8-fold covers : {4,148}*1184, {8,74}*1184, {2,296}*1184
   9-fold covers : {2,333}*1332, {6,111}*1332
   10-fold covers : {10,74}*1480, {2,370}*1480
   11-fold covers : {2,407}*1628
   12-fold covers : {12,74}*1776, {6,148}*1776a, {2,444}*1776, {4,222}*1776a, {6,111}*1776, {4,111}*1776
   13-fold covers : {2,481}*1924
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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