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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,26,2,4}*1664
if this polytope has a name.
Group : SmallGroup(1664,17945)
Rank : 5
Schlafli Type : {4,26,2,4}
Number of vertices, edges, etc : 4, 52, 26, 4, 4
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 : {2,26,2,4}*832, {4,26,2,2}*832
   4-fold quotients : {2,13,2,4}*416, {2,26,2,2}*416
   8-fold quotients : {2,13,2,2}*208
   13-fold quotients : {4,2,2,4}*128
   26-fold quotients : {2,2,2,4}*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 := (27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)
(37,50)(38,51)(39,52);;
s1 := ( 1,27)( 2,39)( 3,38)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,31)
(11,30)(12,29)(13,28)(14,40)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)
(22,45)(23,44)(24,43)(25,42)(26,41);;
s2 := ( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)(18,24)
(19,23)(20,22)(27,28)(29,39)(30,38)(31,37)(32,36)(33,35)(40,41)(42,52)(43,51)
(44,50)(45,49)(46,48);;
s3 := (54,55);;
s4 := (53,54)(55,56);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(56)!(27,40)(28,41)(29,42)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)
(36,49)(37,50)(38,51)(39,52);
s1 := Sym(56)!( 1,27)( 2,39)( 3,38)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)
(10,31)(11,30)(12,29)(13,28)(14,40)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)
(21,46)(22,45)(23,44)(24,43)(25,42)(26,41);
s2 := Sym(56)!( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)
(18,24)(19,23)(20,22)(27,28)(29,39)(30,38)(31,37)(32,36)(33,35)(40,41)(42,52)
(43,51)(44,50)(45,49)(46,48);
s3 := Sym(56)!(54,55);
s4 := Sym(56)!(53,54)(55,56);
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, 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*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
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