Polytope of Type {39,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {39,2}*156
if this polytope has a name.
Group : SmallGroup(156,17)
Rank : 3
Schlafli Type : {39,2}
Number of vertices, edges, etc : 39, 39, 2
Order of s₀s₁s₂ : 78
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {39,2,2} of size 312
   {39,2,3} of size 468
   {39,2,4} of size 624
   {39,2,5} of size 780
   {39,2,6} of size 936
   {39,2,7} of size 1092
   {39,2,8} of size 1248
   {39,2,9} of size 1404
   {39,2,10} of size 1560
   {39,2,11} of size 1716
   {39,2,12} of size 1872
Vertex Figure Of :
   {2,39,2} of size 312
   {4,39,2} of size 624
   {6,39,2} of size 936
   {6,39,2} of size 1248
   {4,39,2} of size 1248
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {13,2}*52
   13-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {78,2}*312
   3-fold covers : {117,2}*468, {39,6}*468
   4-fold covers : {156,2}*624, {78,4}*624a, {39,4}*624
   5-fold covers : {195,2}*780
   6-fold covers : {234,2}*936, {78,6}*936b, {78,6}*936c
   7-fold covers : {273,2}*1092
   8-fold covers : {156,4}*1248a, {312,2}*1248, {78,8}*1248, {39,8}*1248, {78,4}*1248
   9-fold covers : {351,2}*1404, {117,6}*1404, {39,6}*1404
   10-fold covers : {78,10}*1560, {390,2}*1560
   11-fold covers : {429,2}*1716
   12-fold covers : {468,2}*1872, {234,4}*1872a, {117,4}*1872, {78,12}*1872b, {156,6}*1872b, {156,6}*1872c, {78,12}*1872c, {39,12}*1872, {39,6}*1872
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)(38,39);;
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)(37,38);;
s2 := (40,41);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(41)!( 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)(38,39);
s1 := Sym(41)!( 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)(37,38);
s2 := Sym(41)!(40,41);
poly := sub<Sym(41)|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 >;

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