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Polytope of Type {2,2,14,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,14,10}*1120
if this polytope has a name.
Group : SmallGroup(1120,1088)
Rank : 5
Schlafli Type : {2,2,14,10}
Number of vertices, edges, etc : 2, 2, 14, 70, 10
Order of s0s1s2s3s4 : 70
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,14,2}*224
   7-fold quotients : {2,2,2,10}*160
   10-fold quotients : {2,2,7,2}*112
   14-fold quotients : {2,2,2,5}*80
   35-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)
(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)(50,51)
(55,60)(56,59)(57,58)(62,67)(63,66)(64,65)(69,74)(70,73)(71,72);;
s3 := ( 5, 6)( 7,11)( 8,10)(12,34)(13,33)(14,39)(15,38)(16,37)(17,36)(18,35)
(19,27)(20,26)(21,32)(22,31)(23,30)(24,29)(25,28)(40,41)(42,46)(43,45)(47,69)
(48,68)(49,74)(50,73)(51,72)(52,71)(53,70)(54,62)(55,61)(56,67)(57,66)(58,65)
(59,64)(60,63);;
s4 := ( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,40)(13,41)(14,42)
(15,43)(16,44)(17,45)(18,46)(19,68)(20,69)(21,70)(22,71)(23,72)(24,73)(25,74)
(26,61)(27,62)(28,63)(29,64)(30,65)(31,66)(32,67)(33,54)(34,55)(35,56)(36,57)
(37,58)(38,59)(39,60);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!(1,2);
s1 := Sym(74)!(3,4);
s2 := Sym(74)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)
(27,32)(28,31)(29,30)(34,39)(35,38)(36,37)(41,46)(42,45)(43,44)(48,53)(49,52)
(50,51)(55,60)(56,59)(57,58)(62,67)(63,66)(64,65)(69,74)(70,73)(71,72);
s3 := Sym(74)!( 5, 6)( 7,11)( 8,10)(12,34)(13,33)(14,39)(15,38)(16,37)(17,36)
(18,35)(19,27)(20,26)(21,32)(22,31)(23,30)(24,29)(25,28)(40,41)(42,46)(43,45)
(47,69)(48,68)(49,74)(50,73)(51,72)(52,71)(53,70)(54,62)(55,61)(56,67)(57,66)
(58,65)(59,64)(60,63);
s4 := Sym(74)!( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,40)(13,41)
(14,42)(15,43)(16,44)(17,45)(18,46)(19,68)(20,69)(21,70)(22,71)(23,72)(24,73)
(25,74)(26,61)(27,62)(28,63)(29,64)(30,65)(31,66)(32,67)(33,54)(34,55)(35,56)
(36,57)(37,58)(38,59)(39,60);
poly := sub<Sym(74)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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