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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,26}*1664
if this polytope has a name.
Group : SmallGroup(1664,17945)
Rank : 5
Schlafli Type : {4,2,4,26}
Number of vertices, edges, etc : 4, 4, 4, 52, 26
Order of s₀s₁s₂s₃s₄ : 52
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 : {2,2,4,26}*832, {4,2,2,26}*832
   4-fold quotients : {4,2,2,13}*416, {2,2,2,26}*416
   8-fold quotients : {2,2,2,13}*208
   13-fold quotients : {4,2,4,2}*128
   26-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   52-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

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