Polytope of Type {2,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,34}*136
if this polytope has a name.
Group : SmallGroup(136,14)
Rank : 3
Schlafli Type : {2,34}
Number of vertices, edges, etc : 2, 34, 34
Order of s₀s₁s₂ : 34
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,34,2} of size 272
   {2,34,4} of size 544
   {2,34,6} of size 816
   {2,34,8} of size 1088
   {2,34,10} of size 1360
   {2,34,12} of size 1632
   {2,34,14} of size 1904
Vertex Figure Of :
   {2,2,34} of size 272
   {3,2,34} of size 408
   {4,2,34} of size 544
   {5,2,34} of size 680
   {6,2,34} of size 816
   {7,2,34} of size 952
   {8,2,34} of size 1088
   {9,2,34} of size 1224
   {10,2,34} of size 1360
   {11,2,34} of size 1496
   {12,2,34} of size 1632
   {13,2,34} of size 1768
   {14,2,34} of size 1904
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,17}*68
   17-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,68}*272, {4,34}*272
   3-fold covers : {6,34}*408, {2,102}*408
   4-fold covers : {4,68}*544, {2,136}*544, {8,34}*544
   5-fold covers : {10,34}*680, {2,170}*680
   6-fold covers : {12,34}*816, {6,68}*816a, {2,204}*816, {4,102}*816a
   7-fold covers : {14,34}*952, {2,238}*952
   8-fold covers : {8,68}*1088a, {4,136}*1088a, {8,68}*1088b, {4,136}*1088b, {4,68}*1088, {16,34}*1088, {2,272}*1088
   9-fold covers : {18,34}*1224, {2,306}*1224, {6,102}*1224a, {6,102}*1224b, {6,102}*1224c
   10-fold covers : {20,34}*1360, {10,68}*1360, {2,340}*1360, {4,170}*1360
   11-fold covers : {22,34}*1496, {2,374}*1496
   12-fold covers : {24,34}*1632, {6,136}*1632, {12,68}*1632, {4,204}*1632a, {2,408}*1632, {8,102}*1632, {6,68}*1632, {6,102}*1632, {4,102}*1632
   13-fold covers : {26,34}*1768, {2,442}*1768
   14-fold covers : {28,34}*1904, {14,68}*1904, {2,476}*1904, {4,238}*1904
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope