Polytope of Type {3,6,20}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope