Polytope of Type {3,2,28,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,28,4}*1344
if this polytope has a name.
Group : SmallGroup(1344,7765)
Rank : 5
Schlafli Type : {3,2,28,4}
Number of vertices, edges, etc : 3, 3, 28, 56, 4
Order of s₀s₁s₂s₃s₄ : 84
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 : {3,2,28,2}*672, {3,2,14,4}*672
   4-fold quotients : {3,2,14,2}*336
   7-fold quotients : {3,2,4,4}*192
   8-fold quotients : {3,2,7,2}*168
   14-fold quotients : {3,2,2,4}*96, {3,2,4,2}*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)(32,46)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,53)(40,59)
(41,58)(42,57)(43,56)(44,55)(45,54);;
s3 := ( 4,33)( 5,32)( 6,38)( 7,37)( 8,36)( 9,35)(10,34)(11,40)(12,39)(13,45)
(14,44)(15,43)(16,42)(17,41)(18,47)(19,46)(20,52)(21,51)(22,50)(23,49)(24,48)
(25,54)(26,53)(27,59)(28,58)(29,57)(30,56)(31,55);;
s4 := (32,39)(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(46,53)(47,54)(48,55)
(49,56)(50,57)(51,58)(52,59);;
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, 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*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)(32,46)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,53)
(40,59)(41,58)(42,57)(43,56)(44,55)(45,54);
s3 := Sym(59)!( 4,33)( 5,32)( 6,38)( 7,37)( 8,36)( 9,35)(10,34)(11,40)(12,39)
(13,45)(14,44)(15,43)(16,42)(17,41)(18,47)(19,46)(20,52)(21,51)(22,50)(23,49)
(24,48)(25,54)(26,53)(27,59)(28,58)(29,57)(30,56)(31,55);
s4 := Sym(59)!(32,39)(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(46,53)(47,54)
(48,55)(49,56)(50,57)(51,58)(52,59);
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, 
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*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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