Polytope of Type {20,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,238598)
Rank : 4
Schlafli Type : {20,4,3}
Number of vertices, edges, etc : 40, 160, 24, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   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) :
   4-fold quotients : {10,4,3}*480
   5-fold quotients : {4,4,3}*384b
   10-fold quotients : {4,4,3}*192a
   16-fold quotients : {10,2,3}*120
   20-fold quotients : {2,4,3}*96
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {2,4,3}*48
   80-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,65)(18,66)(19,67)(20,68)
(21,70)(22,69)(23,72)(24,71)(25,75)(26,76)(27,73)(28,74)(29,80)(30,79)(31,78)
(32,77)(33,49)(34,50)(35,51)(36,52)(37,54)(38,53)(39,56)(40,55)(41,59)(42,60)
(43,57)(44,58)(45,64)(46,63)(47,62)(48,61);;
s1 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,17)(10,18)
(11,19)(12,20)(13,21)(14,22)(15,23)(16,24)(33,73)(34,74)(35,75)(36,76)(37,77)
(38,78)(39,79)(40,80)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(47,71)(48,72)
(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64);;
s2 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)
(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)(57,61)
(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);;
s3 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)
(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44)(50,52)(53,61)(54,64)
(55,63)(56,62)(58,60)(66,68)(69,77)(70,80)(71,79)(72,78)(74,76);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s3*s2*s3*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,65)(18,66)(19,67)
(20,68)(21,70)(22,69)(23,72)(24,71)(25,75)(26,76)(27,73)(28,74)(29,80)(30,79)
(31,78)(32,77)(33,49)(34,50)(35,51)(36,52)(37,54)(38,53)(39,56)(40,55)(41,59)
(42,60)(43,57)(44,58)(45,64)(46,63)(47,62)(48,61);
s1 := Sym(80)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,17)
(10,18)(11,19)(12,20)(13,21)(14,22)(15,23)(16,24)(33,73)(34,74)(35,75)(36,76)
(37,77)(38,78)(39,79)(40,80)(41,65)(42,66)(43,67)(44,68)(45,69)(46,70)(47,71)
(48,72)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64);
s2 := Sym(80)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)
(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)
(57,61)(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);
s3 := Sym(80)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)
(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44)(50,52)(53,61)
(54,64)(55,63)(56,62)(58,60)(66,68)(69,77)(70,80)(71,79)(72,78)(74,76);
poly := sub<Sym(80)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s3*s2*s3*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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