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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,26,2}*832
if this polytope has a name.
Group : SmallGroup(832,1605)
Rank : 5
Schlafli Type : {2,4,26,2}
Number of vertices, edges, etc : 2, 4, 52, 26, 2
Order of s₀s₁s₂s₃s₄ : 52
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,26,2,2} of size 1664
Vertex Figure Of :
   {2,2,4,26,2} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,26,2}*416
   4-fold quotients : {2,2,13,2}*208
   13-fold quotients : {2,4,2,2}*64
   26-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,26,2}*1664, {2,4,52,2}*1664, {2,4,26,4}*1664, {2,8,26,2}*1664
Permutation Representation (GAP) :

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

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