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Polytope of Type {3,2,4,39}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,39}*1872
if this polytope has a name.
Group : SmallGroup(1872,1036)
Rank : 5
Schlafli Type : {3,2,4,39}
Number of vertices, edges, etc : 3, 3, 4, 78, 39
Order of s0s1s2s3s4 : 39
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   13-fold quotients : {3,2,4,3}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)
(46,47)(48,49)(50,51)(52,53)(54,55);;
s3 := ( 5, 6)( 8,52)( 9,54)(10,53)(11,55)(12,48)(13,50)(14,49)(15,51)(16,44)
(17,46)(18,45)(19,47)(20,40)(21,42)(22,41)(23,43)(24,36)(25,38)(26,37)(27,39)
(28,32)(29,34)(30,33)(31,35);;
s4 := ( 4, 8)( 5, 9)( 6,11)( 7,10)(12,52)(13,53)(14,55)(15,54)(16,48)(17,49)
(18,51)(19,50)(20,44)(21,45)(22,47)(23,46)(24,40)(25,41)(26,43)(27,42)(28,36)
(29,37)(30,39)(31,38)(34,35);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*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*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(55)!(2,3);
s1 := Sym(55)!(1,2);
s2 := Sym(55)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)
(44,45)(46,47)(48,49)(50,51)(52,53)(54,55);
s3 := Sym(55)!( 5, 6)( 8,52)( 9,54)(10,53)(11,55)(12,48)(13,50)(14,49)(15,51)
(16,44)(17,46)(18,45)(19,47)(20,40)(21,42)(22,41)(23,43)(24,36)(25,38)(26,37)
(27,39)(28,32)(29,34)(30,33)(31,35);
s4 := Sym(55)!( 4, 8)( 5, 9)( 6,11)( 7,10)(12,52)(13,53)(14,55)(15,54)(16,48)
(17,49)(18,51)(19,50)(20,44)(21,45)(22,47)(23,46)(24,40)(25,41)(26,43)(27,42)
(28,36)(29,37)(30,39)(31,38)(34,35);
poly := sub<Sym(55)|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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*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*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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