Polytope of Type {37,2}

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

s0 := ( 2, 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);;
s1 := ( 1, 2)( 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);;
s2 := (38,39);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(39)!( 2, 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);
s1 := Sym(39)!( 1, 2)( 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);
s2 := Sym(39)!(38,39);
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*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 >;

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