Polytope of Type {3,2,6,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,14}*1008
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 5
Schlafli Type : {3,2,6,14}
Number of vertices, edges, etc : 3, 3, 6, 42, 14
Order of s₀s₁s₂s₃s₄ : 42
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) :
   3-fold quotients : {3,2,2,14}*336
   6-fold quotients : {3,2,2,7}*168
   7-fold quotients : {3,2,6,2}*144
   14-fold quotients : {3,2,3,2}*72
   21-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,60)(12,61)(13,62)
(14,63)(15,64)(16,65)(17,66)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)(24,59)
(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,81)(33,82)(34,83)(35,84)
(36,85)(37,86)(38,87)(39,74)(40,75)(41,76)(42,77)(43,78)(44,79)(45,80);;
s3 := ( 4,53)( 5,59)( 6,58)( 7,57)( 8,56)( 9,55)(10,54)(11,46)(12,52)(13,51)
(14,50)(15,49)(16,48)(17,47)(18,60)(19,66)(20,65)(21,64)(22,63)(23,62)(24,61)
(25,74)(26,80)(27,79)(28,78)(29,77)(30,76)(31,75)(32,67)(33,73)(34,72)(35,71)
(36,70)(37,69)(38,68)(39,81)(40,87)(41,86)(42,85)(43,84)(44,83)(45,82);;
s4 := ( 4,26)( 5,25)( 6,31)( 7,30)( 8,29)( 9,28)(10,27)(11,33)(12,32)(13,38)
(14,37)(15,36)(16,35)(17,34)(18,40)(19,39)(20,45)(21,44)(22,43)(23,42)(24,41)
(46,68)(47,67)(48,73)(49,72)(50,71)(51,70)(52,69)(53,75)(54,74)(55,80)(56,79)
(57,78)(58,77)(59,76)(60,82)(61,81)(62,87)(63,86)(64,85)(65,84)(66,83);;
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(87)!(2,3);
s1 := Sym(87)!(1,2);
s2 := Sym(87)!( 4,46)( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,60)(12,61)
(13,62)(14,63)(15,64)(16,65)(17,66)(18,53)(19,54)(20,55)(21,56)(22,57)(23,58)
(24,59)(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,81)(33,82)(34,83)
(35,84)(36,85)(37,86)(38,87)(39,74)(40,75)(41,76)(42,77)(43,78)(44,79)(45,80);
s3 := Sym(87)!( 4,53)( 5,59)( 6,58)( 7,57)( 8,56)( 9,55)(10,54)(11,46)(12,52)
(13,51)(14,50)(15,49)(16,48)(17,47)(18,60)(19,66)(20,65)(21,64)(22,63)(23,62)
(24,61)(25,74)(26,80)(27,79)(28,78)(29,77)(30,76)(31,75)(32,67)(33,73)(34,72)
(35,71)(36,70)(37,69)(38,68)(39,81)(40,87)(41,86)(42,85)(43,84)(44,83)(45,82);
s4 := Sym(87)!( 4,26)( 5,25)( 6,31)( 7,30)( 8,29)( 9,28)(10,27)(11,33)(12,32)
(13,38)(14,37)(15,36)(16,35)(17,34)(18,40)(19,39)(20,45)(21,44)(22,43)(23,42)
(24,41)(46,68)(47,67)(48,73)(49,72)(50,71)(51,70)(52,69)(53,75)(54,74)(55,80)
(56,79)(57,78)(58,77)(59,76)(60,82)(61,81)(62,87)(63,86)(64,85)(65,84)(66,83);
poly := sub<Sym(87)|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, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope