Polytope of Type {3,2,14,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,14,4,2}*1344
if this polytope has a name.
Group : SmallGroup(1344,11527)
Rank : 6
Schlafli Type : {3,2,14,4,2}
Number of vertices, edges, etc : 3, 3, 14, 28, 4, 2
Order of s₀s₁s₂s₃s₄s₅ : 84
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   2-fold quotients : {3,2,14,2,2}*672
   4-fold quotients : {3,2,7,2,2}*336
   7-fold quotients : {3,2,2,4,2}*192
   14-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 9,10)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)
(28,29)(30,31);;
s3 := ( 4, 6)( 5,14)( 7,11)( 8, 9)(10,22)(12,18)(13,20)(15,16)(17,28)(21,26)
(23,24)(25,29)(27,30);;
s4 := ( 4, 5)( 6, 9)( 7,10)( 8,13)(11,16)(12,17)(14,20)(15,21)(18,24)(19,25)
(22,26)(23,27)(28,30)(29,31);;
s5 := (32,33);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
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(33)!(2,3);
s1 := Sym(33)!(1,2);
s2 := Sym(33)!( 6, 7)( 9,10)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)
(26,27)(28,29)(30,31);
s3 := Sym(33)!( 4, 6)( 5,14)( 7,11)( 8, 9)(10,22)(12,18)(13,20)(15,16)(17,28)
(21,26)(23,24)(25,29)(27,30);
s4 := Sym(33)!( 4, 5)( 6, 9)( 7,10)( 8,13)(11,16)(12,17)(14,20)(15,21)(18,24)
(19,25)(22,26)(23,27)(28,30)(29,31);
s5 := Sym(33)!(32,33);
poly := sub<Sym(33)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
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 >;

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