Polytope of Type {34,2}

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

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

Permutation Representation (Magma) :

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

to this polytope