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

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

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