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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,6,3}*1008
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 5
Schlafli Type : {2,14,6,3}
Number of vertices, edges, etc : 2, 14, 42, 9, 3
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 : {2,14,2,3}*336
   6-fold quotients : {2,7,2,3}*168
   7-fold quotients : {2,2,6,3}*144
   21-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)(25,30)
(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)(48,49)
(53,58)(54,57)(55,56)(60,65)(61,64)(62,63);;
s2 := ( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)(16,19)
(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)(45,46)
(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61);;
s3 := ( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,52)(25,53)(26,54)
(27,55)(28,56)(29,57)(30,58)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)
(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65);;
s4 := ( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,38)(11,39)(12,40)
(13,41)(14,42)(15,43)(16,44)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)(23,37)
(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(65)!(1,2);
s1 := Sym(65)!( 4, 9)( 5, 8)( 6, 7)(11,16)(12,15)(13,14)(18,23)(19,22)(20,21)
(25,30)(26,29)(27,28)(32,37)(33,36)(34,35)(39,44)(40,43)(41,42)(46,51)(47,50)
(48,49)(53,58)(54,57)(55,56)(60,65)(61,64)(62,63);
s2 := Sym(65)!( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)
(16,19)(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)
(45,46)(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61);
s3 := Sym(65)!( 3,10)( 4,11)( 5,12)( 6,13)( 7,14)( 8,15)( 9,16)(24,52)(25,53)
(26,54)(27,55)(28,56)(29,57)(30,58)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)
(37,51)(38,59)(39,60)(40,61)(41,62)(42,63)(43,64)(44,65);
s4 := Sym(65)!( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,38)(11,39)
(12,40)(13,41)(14,42)(15,43)(16,44)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)
(23,37)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65);
poly := sub<Sym(65)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope