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Polytope of Type {2,2,4,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,38}*1216
if this polytope has a name.
Group : SmallGroup(1216,1369)
Rank : 5
Schlafli Type : {2,2,4,38}
Number of vertices, edges, etc : 2, 2, 4, 76, 38
Order of s0s1s2s3s4 : 76
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 : {2,2,2,38}*608
   4-fold quotients : {2,2,2,19}*304
   19-fold quotients : {2,2,4,2}*64
   38-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)(52,71)
(53,72)(54,73)(55,74)(56,75)(57,76)(58,77)(59,78)(60,79)(61,80);;
s3 := ( 5,43)( 6,61)( 7,60)( 8,59)( 9,58)(10,57)(11,56)(12,55)(13,54)(14,53)
(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,62)(25,80)
(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)(36,69)
(37,68)(38,67)(39,66)(40,65)(41,64)(42,63);;
s4 := ( 5, 6)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(24,25)
(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(43,44)(45,61)(46,60)
(47,59)(48,58)(49,57)(50,56)(51,55)(52,54)(62,63)(64,80)(65,79)(66,78)(67,77)
(68,76)(69,75)(70,74)(71,73);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(80)!(1,2);
s1 := Sym(80)!(3,4);
s2 := Sym(80)!(43,62)(44,63)(45,64)(46,65)(47,66)(48,67)(49,68)(50,69)(51,70)
(52,71)(53,72)(54,73)(55,74)(56,75)(57,76)(58,77)(59,78)(60,79)(61,80);
s3 := Sym(80)!( 5,43)( 6,61)( 7,60)( 8,59)( 9,58)(10,57)(11,56)(12,55)(13,54)
(14,53)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,62)
(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(35,70)
(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63);
s4 := Sym(80)!( 5, 6)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)
(24,25)(26,42)(27,41)(28,40)(29,39)(30,38)(31,37)(32,36)(33,35)(43,44)(45,61)
(46,60)(47,59)(48,58)(49,57)(50,56)(51,55)(52,54)(62,63)(64,80)(65,79)(66,78)
(67,77)(68,76)(69,75)(70,74)(71,73);
poly := sub<Sym(80)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*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 >; 
 

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