Polytope of Type {2,35}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,35}*140
if this polytope has a name.
Group : SmallGroup(140,10)
Rank : 3
Schlafli Type : {2,35}
Number of vertices, edges, etc : 2, 35, 35
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 :
   {2,35,2} of size 280
   {2,35,10} of size 1400
   {2,35,6} of size 1680
   {2,35,10} of size 1680
   {2,35,14} of size 1960
Vertex Figure Of :
   {2,2,35} of size 280
   {3,2,35} of size 420
   {4,2,35} of size 560
   {5,2,35} of size 700
   {6,2,35} of size 840
   {7,2,35} of size 980
   {8,2,35} of size 1120
   {9,2,35} of size 1260
   {10,2,35} of size 1400
   {11,2,35} of size 1540
   {12,2,35} of size 1680
   {13,2,35} of size 1820
   {14,2,35} of size 1960
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,7}*28
   7-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,70}*280
   3-fold covers : {2,105}*420
   4-fold covers : {2,140}*560, {4,70}*560
   5-fold covers : {2,175}*700, {10,35}*700
   6-fold covers : {6,70}*840, {2,210}*840
   7-fold covers : {2,245}*980, {14,35}*980
   8-fold covers : {4,140}*1120, {2,280}*1120, {8,70}*1120
   9-fold covers : {2,315}*1260, {6,105}*1260
   10-fold covers : {2,350}*1400, {10,70}*1400b, {10,70}*1400c
   11-fold covers : {2,385}*1540
   12-fold covers : {12,70}*1680, {6,140}*1680a, {2,420}*1680, {4,210}*1680a, {6,105}*1680, {4,105}*1680
   13-fold covers : {2,455}*1820
   14-fold covers : {2,490}*1960, {14,70}*1960b, {14,70}*1960c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(37)!(1,2);
s1 := Sym(37)!( 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);
s2 := Sym(37)!( 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);
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*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*s1*s2 >;

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