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Polytope of Type {70}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70}*140
Also Known As : 70-gon, {70}. if this polytope has another name.
Group : SmallGroup(140,10)
Rank : 2
Schlafli Type : {70}
Number of vertices, edges, etc : 70, 70
Order of s0s1 : 70
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {70,2} of size 280
   {70,4} of size 560
   {70,6} of size 840
   {70,8} of size 1120
   {70,10} of size 1400
   {70,10} of size 1400
   {70,10} of size 1400
   {70,12} of size 1680
   {70,6} of size 1680
   {70,6} of size 1680
   {70,10} of size 1680
   {70,10} of size 1680
   {70,14} of size 1960
   {70,14} of size 1960
   {70,14} of size 1960
Vertex Figure Of :
   {2,70} of size 280
   {4,70} of size 560
   {6,70} of size 840
   {8,70} of size 1120
   {10,70} of size 1400
   {10,70} of size 1400
   {10,70} of size 1400
   {12,70} of size 1680
   {6,70} of size 1680
   {6,70} of size 1680
   {10,70} of size 1680
   {10,70} of size 1680
   {14,70} of size 1960
   {14,70} of size 1960
   {14,70} of size 1960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {35}*70
   5-fold quotients : {14}*28
   7-fold quotients : {10}*20
   10-fold quotients : {7}*14
   14-fold quotients : {5}*10
   35-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {140}*280
   3-fold covers : {210}*420
   4-fold covers : {280}*560
   5-fold covers : {350}*700
   6-fold covers : {420}*840
   7-fold covers : {490}*980
   8-fold covers : {560}*1120
   9-fold covers : {630}*1260
   10-fold covers : {700}*1400
   11-fold covers : {770}*1540
   12-fold covers : {840}*1680
   13-fold covers : {910}*1820
   14-fold covers : {980}*1960
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,29)( 9,35)(10,34)(11,33)(12,32)(13,31)(14,30)
(15,22)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)(37,42)(38,41)(39,40)(43,64)
(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,57)(51,63)(52,62)(53,61)(54,60)
(55,59)(56,58);;
s1 := ( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,37)( 9,36)(10,42)
(11,41)(12,40)(13,39)(14,38)(15,65)(16,64)(17,70)(18,69)(19,68)(20,67)(21,66)
(22,58)(23,57)(24,63)(25,62)(26,61)(27,60)(28,59)(29,51)(30,50)(31,56)(32,55)
(33,54)(34,53)(35,52);;
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*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(70)!( 2, 7)( 3, 6)( 4, 5)( 8,29)( 9,35)(10,34)(11,33)(12,32)(13,31)
(14,30)(15,22)(16,28)(17,27)(18,26)(19,25)(20,24)(21,23)(37,42)(38,41)(39,40)
(43,64)(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,57)(51,63)(52,62)(53,61)
(54,60)(55,59)(56,58);
s1 := Sym(70)!( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,37)( 9,36)
(10,42)(11,41)(12,40)(13,39)(14,38)(15,65)(16,64)(17,70)(18,69)(19,68)(20,67)
(21,66)(22,58)(23,57)(24,63)(25,62)(26,61)(27,60)(28,59)(29,51)(30,50)(31,56)
(32,55)(33,54)(34,53)(35,52);
poly := sub<Sym(70)|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*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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