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Polytope of Type {35}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35}*70
Also Known As : 35-gon, {35}. if this polytope has another name.
Group : SmallGroup(70,3)
Rank : 2
Schlafli Type : {35}
Number of vertices, edges, etc : 35, 35
Order of s0s1 : 35
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {35,2} of size 140
   {35,10} of size 700
   {35,6} of size 840
   {35,10} of size 840
   {35,14} of size 980
   {35,4} of size 1120
   {35,6} of size 1680
   {35,8} of size 1680
   {35,8} of size 1680
   {35,4} of size 1680
   {35,6} of size 1680
   {35,6} of size 1680
   {35,10} of size 1680
Vertex Figure Of :
   {2,35} of size 140
   {10,35} of size 700
   {6,35} of size 840
   {10,35} of size 840
   {14,35} of size 980
   {4,35} of size 1120
   {6,35} of size 1680
   {8,35} of size 1680
   {8,35} of size 1680
   {4,35} of size 1680
   {6,35} of size 1680
   {6,35} of size 1680
   {10,35} of size 1680
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {7}*14
   7-fold quotients : {5}*10
Covers (Minimal Covers in Boldface) :
   2-fold covers : {70}*140
   3-fold covers : {105}*210
   4-fold covers : {140}*280
   5-fold covers : {175}*350
   6-fold covers : {210}*420
   7-fold covers : {245}*490
   8-fold covers : {280}*560
   9-fold covers : {315}*630
   10-fold covers : {350}*700
   11-fold covers : {385}*770
   12-fold covers : {420}*840
   13-fold covers : {455}*910
   14-fold covers : {490}*980
   15-fold covers : {525}*1050
   16-fold covers : {560}*1120
   17-fold covers : {595}*1190
   18-fold covers : {630}*1260
   19-fold covers : {665}*1330
   20-fold covers : {700}*1400
   21-fold covers : {735}*1470
   22-fold covers : {770}*1540
   23-fold covers : {805}*1610
   24-fold covers : {840}*1680
   25-fold covers : {875}*1750
   26-fold covers : {910}*1820
   27-fold covers : {945}*1890
   28-fold covers : {980}*1960
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);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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(35)!( 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(35)!( 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);
poly := sub<Sym(35)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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 >; 
 
References : None.
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