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Polytope of Type {3,2,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,20,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,151308)
Rank : 5
Schlafli Type : {3,2,20,4}
Number of vertices, edges, etc : 3, 3, 40, 80, 8
Order of s0s1s2s3s4 : 60
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 : {3,2,20,4}*960
   4-fold quotients : {3,2,20,2}*480, {3,2,10,4}*480
   5-fold quotients : {3,2,4,4}*384
   8-fold quotients : {3,2,10,2}*240
   10-fold quotients : {3,2,4,4}*192
   16-fold quotients : {3,2,5,2}*120
   20-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
   40-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 6, 7)(10,13)(11,12)(14,19)(15,23)(16,22)(17,21)(18,20)(25,28)
(26,27)(30,33)(31,32)(34,39)(35,43)(36,42)(37,41)(38,40)(44,64)(45,68)(46,67)
(47,66)(48,65)(49,69)(50,73)(51,72)(52,71)(53,70)(54,79)(55,83)(56,82)(57,81)
(58,80)(59,74)(60,78)(61,77)(62,76)(63,75);;
s3 := ( 4,45)( 5,44)( 6,48)( 7,47)( 8,46)( 9,50)(10,49)(11,53)(12,52)(13,51)
(14,55)(15,54)(16,58)(17,57)(18,56)(19,60)(20,59)(21,63)(22,62)(23,61)(24,65)
(25,64)(26,68)(27,67)(28,66)(29,70)(30,69)(31,73)(32,72)(33,71)(34,75)(35,74)
(36,78)(37,77)(38,76)(39,80)(40,79)(41,83)(42,82)(43,81);;
s4 := (24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)(38,43)
(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(64,79)
(65,80)(66,81)(67,82)(68,83)(69,74)(70,75)(71,76)(72,77)(73,78);;
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*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(83)!(2,3);
s1 := Sym(83)!(1,2);
s2 := Sym(83)!( 5, 8)( 6, 7)(10,13)(11,12)(14,19)(15,23)(16,22)(17,21)(18,20)
(25,28)(26,27)(30,33)(31,32)(34,39)(35,43)(36,42)(37,41)(38,40)(44,64)(45,68)
(46,67)(47,66)(48,65)(49,69)(50,73)(51,72)(52,71)(53,70)(54,79)(55,83)(56,82)
(57,81)(58,80)(59,74)(60,78)(61,77)(62,76)(63,75);
s3 := Sym(83)!( 4,45)( 5,44)( 6,48)( 7,47)( 8,46)( 9,50)(10,49)(11,53)(12,52)
(13,51)(14,55)(15,54)(16,58)(17,57)(18,56)(19,60)(20,59)(21,63)(22,62)(23,61)
(24,65)(25,64)(26,68)(27,67)(28,66)(29,70)(30,69)(31,73)(32,72)(33,71)(34,75)
(35,74)(36,78)(37,77)(38,76)(39,80)(40,79)(41,83)(42,82)(43,81);
s4 := Sym(83)!(24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)
(38,43)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)
(64,79)(65,80)(66,81)(67,82)(68,83)(69,74)(70,75)(71,76)(72,77)(73,78);
poly := sub<Sym(83)|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, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*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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