Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,6,4,2}

Atlas Canonical Name {20,6,4,2}*1920c

Overview

Group
SmallGroup(1920,240408)
Rank
5
Schläfli Type
{20,6,4,2}
Vertices, edges, …
20, 60, 12, 4, 2
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

10-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,49)(42,50)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)(10,23)(11,22)(12,24)(13,29)(14,31)(15,30)(16,32)(33,65)(34,67)(35,66)(36,68)(37,73)(38,75)(39,74)(40,76)(41,69)(42,71)(43,70)(44,72)(45,77)(46,79)(47,78)(48,80)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63);;
s2 := ( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(19,20)(21,29)(22,30)(23,32)(24,31)(27,28)(35,36)(37,45)(38,46)(39,48)(40,47)(43,44)(51,52)(53,61)(54,62)(55,64)(56,63)(59,60)(67,68)(69,77)(70,78)(71,80)(72,79)(75,76);;
s3 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79);;
s4 := (81,82);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(82)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,49)(42,50)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56);
s1 := Sym(82)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,25)( 6,27)( 7,26)( 8,28)( 9,21)(10,23)(11,22)(12,24)(13,29)(14,31)(15,30)(16,32)(33,65)(34,67)(35,66)(36,68)(37,73)(38,75)(39,74)(40,76)(41,69)(42,71)(43,70)(44,72)(45,77)(46,79)(47,78)(48,80)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63);
s2 := Sym(82)!( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)(11,12)(19,20)(21,29)(22,30)(23,32)(24,31)(27,28)(35,36)(37,45)(38,46)(39,48)(40,47)(43,44)(51,52)(53,61)(54,62)(55,64)(56,63)(59,60)(67,68)(69,77)(70,78)(71,80)(72,79)(75,76);
s3 := Sym(82)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71)(73,76)(74,75)(77,80)(78,79);
s4 := Sym(82)!(81,82);
poly := sub<Sym(82)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 >;