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Polytope of Type {4,2,14,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,14,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,11527)
Rank : 5
Schlafli Type : {4,2,14,6}
Number of vertices, edges, etc : 4, 4, 14, 42, 6
Order of s0s1s2s3s4 : 84
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) :
   2-fold quotients : {2,2,14,6}*672
   3-fold quotients : {4,2,14,2}*448
   6-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
   7-fold quotients : {4,2,2,6}*192
   12-fold quotients : {2,2,7,2}*112
   14-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   21-fold quotients : {4,2,2,2}*64
   28-fold quotients : {2,2,2,3}*48
   42-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(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)(76,81)(77,80)
(78,79)(83,88)(84,87)(85,86);;
s3 := ( 5,48)( 6,47)( 7,53)( 8,52)( 9,51)(10,50)(11,49)(12,62)(13,61)(14,67)
(15,66)(16,65)(17,64)(18,63)(19,55)(20,54)(21,60)(22,59)(23,58)(24,57)(25,56)
(26,69)(27,68)(28,74)(29,73)(30,72)(31,71)(32,70)(33,83)(34,82)(35,88)(36,87)
(37,86)(38,85)(39,84)(40,76)(41,75)(42,81)(43,80)(44,79)(45,78)(46,77);;
s4 := ( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,81)(12,68)(13,69)(14,70)
(15,71)(16,72)(17,73)(18,74)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,88)
(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,47)(34,48)(35,49)(36,50)
(37,51)(38,52)(39,53)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67);;
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
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(88)!(2,3);
s1 := Sym(88)!(1,2)(3,4);
s2 := Sym(88)!( 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)(76,81)
(77,80)(78,79)(83,88)(84,87)(85,86);
s3 := Sym(88)!( 5,48)( 6,47)( 7,53)( 8,52)( 9,51)(10,50)(11,49)(12,62)(13,61)
(14,67)(15,66)(16,65)(17,64)(18,63)(19,55)(20,54)(21,60)(22,59)(23,58)(24,57)
(25,56)(26,69)(27,68)(28,74)(29,73)(30,72)(31,71)(32,70)(33,83)(34,82)(35,88)
(36,87)(37,86)(38,85)(39,84)(40,76)(41,75)(42,81)(43,80)(44,79)(45,78)(46,77);
s4 := Sym(88)!( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,81)(12,68)(13,69)
(14,70)(15,71)(16,72)(17,73)(18,74)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)
(25,88)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,47)(34,48)(35,49)
(36,50)(37,51)(38,52)(39,53)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67);
poly := sub<Sym(88)|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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, 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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