Polytope of Type {14,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,6,3}*1512
Also Known As : {{14,6|2},{6,3}₆}. if this polytope has another name.
Group : SmallGroup(1512,486)
Rank : 4
Schlafli Type : {14,6,3}
Number of vertices, edges, etc : 14, 126, 27, 9
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {14,6,3}*504
   7-fold quotients : {2,6,3}*216
   9-fold quotients : {14,2,3}*168
   18-fold quotients : {7,2,3}*84
   21-fold quotients : {2,6,3}*72
   63-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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