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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,14,6}*1008
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 5
Schlafli Type : {3,2,14,6}
Number of vertices, edges, etc : 3, 3, 14, 42, 6
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 : {3,2,14,2}*336
   6-fold quotients : {3,2,7,2}*168
   7-fold quotients : {3,2,2,6}*144
   14-fold quotients : {3,2,2,3}*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 := ( 5,10)( 6, 9)( 7, 8)(12,17)(13,16)(14,15)(19,24)(20,23)(21,22)(26,31)
(27,30)(28,29)(33,38)(34,37)(35,36)(40,45)(41,44)(42,43)(47,52)(48,51)(49,50)
(54,59)(55,58)(56,57)(61,66)(62,65)(63,64)(68,73)(69,72)(70,71)(75,80)(76,79)
(77,78)(82,87)(83,86)(84,85);;
s3 := ( 4,47)( 5,46)( 6,52)( 7,51)( 8,50)( 9,49)(10,48)(11,61)(12,60)(13,66)
(14,65)(15,64)(16,63)(17,62)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)(24,55)
(25,68)(26,67)(27,73)(28,72)(29,71)(30,70)(31,69)(32,82)(33,81)(34,87)(35,86)
(36,85)(37,84)(38,83)(39,75)(40,74)(41,80)(42,79)(43,78)(44,77)(45,76);;
s4 := ( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,67)(12,68)(13,69)
(14,70)(15,71)(16,72)(17,73)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)
(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,46)(33,47)(34,48)(35,49)
(36,50)(37,51)(38,52)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66);;
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, 
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(87)!(2,3);
s1 := Sym(87)!(1,2);
s2 := Sym(87)!( 5,10)( 6, 9)( 7, 8)(12,17)(13,16)(14,15)(19,24)(20,23)(21,22)
(26,31)(27,30)(28,29)(33,38)(34,37)(35,36)(40,45)(41,44)(42,43)(47,52)(48,51)
(49,50)(54,59)(55,58)(56,57)(61,66)(62,65)(63,64)(68,73)(69,72)(70,71)(75,80)
(76,79)(77,78)(82,87)(83,86)(84,85);
s3 := Sym(87)!( 4,47)( 5,46)( 6,52)( 7,51)( 8,50)( 9,49)(10,48)(11,61)(12,60)
(13,66)(14,65)(15,64)(16,63)(17,62)(18,54)(19,53)(20,59)(21,58)(22,57)(23,56)
(24,55)(25,68)(26,67)(27,73)(28,72)(29,71)(30,70)(31,69)(32,82)(33,81)(34,87)
(35,86)(36,85)(37,84)(38,83)(39,75)(40,74)(41,80)(42,79)(43,78)(44,77)(45,76);
s4 := Sym(87)!( 4,74)( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,67)(12,68)
(13,69)(14,70)(15,71)(16,72)(17,73)(18,81)(19,82)(20,83)(21,84)(22,85)(23,86)
(24,87)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,46)(33,47)(34,48)
(35,49)(36,50)(37,51)(38,52)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66);
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, 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 >;

to this polytope