Polytope of Type {2,2,2,26,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,26,4}*1664
if this polytope has a name.
Group : SmallGroup(1664,19301)
Rank : 6
Schlafli Type : {2,2,2,26,4}
Number of vertices, edges, etc : 2, 2, 2, 26, 52, 4
Order of s₀s₁s₂s₃s₄s₅ : 52
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 : {2,2,2,26,2}*832
   4-fold quotients : {2,2,2,13,2}*416
   13-fold quotients : {2,2,2,2,4}*128
   26-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8,19)( 9,18)(10,17)(11,16)(12,15)(13,14)(21,32)(22,31)(23,30)(24,29)
(25,28)(26,27)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(47,58)(48,57)(49,56)
(50,55)(51,54)(52,53);;
s4 := ( 7, 8)( 9,19)(10,18)(11,17)(12,16)(13,15)(20,21)(22,32)(23,31)(24,30)
(25,29)(26,28)(33,47)(34,46)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)(41,52)
(42,51)(43,50)(44,49)(45,48);;
s5 := ( 7,33)( 8,34)( 9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)
(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)(27,53)
(28,54)(29,55)(30,56)(31,57)(32,58);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(58)!(1,2);
s1 := Sym(58)!(3,4);
s2 := Sym(58)!(5,6);
s3 := Sym(58)!( 8,19)( 9,18)(10,17)(11,16)(12,15)(13,14)(21,32)(22,31)(23,30)
(24,29)(25,28)(26,27)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)(47,58)(48,57)
(49,56)(50,55)(51,54)(52,53);
s4 := Sym(58)!( 7, 8)( 9,19)(10,18)(11,17)(12,16)(13,15)(20,21)(22,32)(23,31)
(24,30)(25,29)(26,28)(33,47)(34,46)(35,58)(36,57)(37,56)(38,55)(39,54)(40,53)
(41,52)(42,51)(43,50)(44,49)(45,48);
s5 := Sym(58)!( 7,33)( 8,34)( 9,35)(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)
(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)(25,51)(26,52)
(27,53)(28,54)(29,55)(30,56)(31,57)(32,58);
poly := sub<Sym(58)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope