Polytope of Type {3,2,14,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,14,8}*1344
if this polytope has a name.
Group : SmallGroup(1344,8561)
Rank : 5
Schlafli Type : {3,2,14,8}
Number of vertices, edges, etc : 3, 3, 14, 56, 8
Order of s₀s₁s₂s₃s₄ : 168
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) :
   2-fold quotients : {3,2,14,4}*672
   4-fold quotients : {3,2,14,2}*336
   7-fold quotients : {3,2,2,8}*192
   8-fold quotients : {3,2,7,2}*168
   14-fold quotients : {3,2,2,4}*96
   28-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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