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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,4,26}*1664
if this polytope has a name.
Group : SmallGroup(1664,19301)
Rank : 6
Schlafli Type : {2,2,2,4,26}
Number of vertices, edges, etc : 2, 2, 2, 4, 52, 26
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 : {2,2,2,2,26}*832
   4-fold quotients : {2,2,2,2,13}*416
   13-fold quotients : {2,2,2,4,2}*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 := (33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(41,54)(42,55)
(43,56)(44,57)(45,58);;
s4 := ( 7,33)( 8,45)( 9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)
(17,36)(18,35)(19,34)(20,46)(21,58)(22,57)(23,56)(24,55)(25,54)(26,53)(27,52)
(28,51)(29,50)(30,49)(31,48)(32,47);;
s5 := ( 7, 8)( 9,19)(10,18)(11,17)(12,16)(13,15)(20,21)(22,32)(23,31)(24,30)
(25,29)(26,28)(33,34)(35,45)(36,44)(37,43)(38,42)(39,41)(46,47)(48,58)(49,57)
(50,56)(51,55)(52,54);;
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*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope