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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,26,4,2}*1664
if this polytope has a name.
Group : SmallGroup(1664,19301)
Rank : 6
Schlafli Type : {2,2,26,4,2}
Number of vertices, edges, etc : 2, 2, 26, 52, 4, 2
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 : {2,2,26,2,2}*832
   4-fold quotients : {2,2,13,2,2}*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 := ( 6,17)( 7,16)( 8,15)( 9,14)(10,13)(11,12)(19,30)(20,29)(21,28)(22,27)
(23,26)(24,25)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)(45,56)(46,55)(47,54)
(48,53)(49,52)(50,51);;
s3 := ( 5, 6)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(18,19)(20,30)(21,29)(22,28)
(23,27)(24,26)(31,45)(32,44)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)
(40,49)(41,48)(42,47)(43,46);;
s4 := ( 5,31)( 6,32)( 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);;
s5 := (57,58);;
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, 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, 
s4*s5*s4*s5, 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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope