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

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

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