Polytope of Type {4,2,2,52}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,52}*1664
if this polytope has a name.
Group : SmallGroup(1664,17950)
Rank : 5
Schlafli Type : {4,2,2,52}
Number of vertices, edges, etc : 4, 4, 2, 52, 52
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 : {2,2,2,52}*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 : {4,2,2,4}*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 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26)(27,28)
(29,32)(30,31)(33,34)(35,36)(37,40)(38,39)(41,42)(43,44)(45,48)(46,47)(49,50)
(51,52)(53,56)(54,55)(57,58);;
s4 := ( 7,13)( 8,10)( 9,19)(11,21)(12,15)(14,17)(16,27)(18,29)(20,23)(22,25)
(24,35)(26,37)(28,31)(30,33)(32,43)(34,45)(36,39)(38,41)(40,51)(42,53)(44,47)
(46,49)(48,57)(50,54)(52,55)(56,58);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
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*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)!(2,3);
s1 := Sym(58)!(1,2)(3,4);
s2 := Sym(58)!(5,6);
s3 := Sym(58)!( 8, 9)(10,11)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26)
(27,28)(29,32)(30,31)(33,34)(35,36)(37,40)(38,39)(41,42)(43,44)(45,48)(46,47)
(49,50)(51,52)(53,56)(54,55)(57,58);
s4 := Sym(58)!( 7,13)( 8,10)( 9,19)(11,21)(12,15)(14,17)(16,27)(18,29)(20,23)
(22,25)(24,35)(26,37)(28,31)(30,33)(32,43)(34,45)(36,39)(38,41)(40,51)(42,53)
(44,47)(46,49)(48,57)(50,54)(52,55)(56,58);
poly := sub<Sym(58)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, 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*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