Polytope of Type {35,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,2}*140
if this polytope has a name.
Group : SmallGroup(140,10)
Rank : 3
Schlafli Type : {35,2}
Number of vertices, edges, etc : 35, 35, 2
Order of s₀s₁s₂ : 70
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {35,2,2} of size 280
   {35,2,3} of size 420
   {35,2,4} of size 560
   {35,2,5} of size 700
   {35,2,6} of size 840
   {35,2,7} of size 980
   {35,2,8} of size 1120
   {35,2,9} of size 1260
   {35,2,10} of size 1400
   {35,2,11} of size 1540
   {35,2,12} of size 1680
   {35,2,13} of size 1820
   {35,2,14} of size 1960
Vertex Figure Of :
   {2,35,2} of size 280
   {10,35,2} of size 1400
   {6,35,2} of size 1680
   {10,35,2} of size 1680
   {14,35,2} of size 1960
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {7,2}*28
   7-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {70,2}*280
   3-fold covers : {105,2}*420
   4-fold covers : {140,2}*560, {70,4}*560
   5-fold covers : {175,2}*700, {35,10}*700
   6-fold covers : {70,6}*840, {210,2}*840
   7-fold covers : {245,2}*980, {35,14}*980
   8-fold covers : {140,4}*1120, {280,2}*1120, {70,8}*1120
   9-fold covers : {315,2}*1260, {105,6}*1260
   10-fold covers : {350,2}*1400, {70,10}*1400b, {70,10}*1400c
   11-fold covers : {385,2}*1540
   12-fold covers : {70,12}*1680, {140,6}*1680a, {420,2}*1680, {210,4}*1680a, {105,6}*1680, {105,4}*1680
   13-fold covers : {455,2}*1820
   14-fold covers : {490,2}*1960, {70,14}*1960b, {70,14}*1960c
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);;
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);;
s2 := (36,37);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(37)!( 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);
s1 := Sym(37)!( 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);
s2 := Sym(37)!(36,37);
poly := sub<Sym(37)|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 >;

to this polytope