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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,28,2,3}*1344
if this polytope has a name.
Group : SmallGroup(1344,7765)
Rank : 5
Schlafli Type : {4,28,2,3}
Number of vertices, edges, etc : 4, 56, 28, 3, 3
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 : {2,28,2,3}*672, {4,14,2,3}*672
   4-fold quotients : {2,14,2,3}*336
   7-fold quotients : {4,4,2,3}*192
   8-fold quotients : {2,7,2,3}*168
   14-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96
   28-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope