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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,26,4}*1664
if this polytope has a name.
Group : SmallGroup(1664,17945)
Rank : 5
Schlafli Type : {4,2,26,4}
Number of vertices, edges, etc : 4, 4, 26, 52, 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 : {2,2,26,4}*832, {4,2,26,2}*832
   4-fold quotients : {4,2,13,2}*416, {2,2,26,2}*416
   8-fold quotients : {2,2,13,2}*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 := (2,3);;
s1 := (1,2)(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);;
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*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(56)!(2,3);
s1 := Sym(56)!(1,2)(3,4);
s2 := Sym(56)!( 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(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)(31,45)(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(56)!( 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);
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*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 >; 
 

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