Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,4,3}

Atlas Canonical Name {20,4,3}*1920

Overview

Group
SmallGroup(1920,238598)
Rank
4
Schläfli Type
{20,4,3}
Vertices, edges, …
40, 160, 24, 6
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

5-fold

10-fold

16-fold

20-fold

32-fold

40-fold

80-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1*s2*s1)^2> of order 2

6 facets

20 vertex figures

P/N, where N=<(s1*s2)^2, s0*s1*s2*s1*s0*s2> of order 4

4 facets

20 vertex figures

  • 20 of 2-fold non-regular quotient of {4,3}*48

Representations

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, 
s0*s1*s0*s1*s0*s1*s0*s1*s3*s0*s1*s0*s2*s3*s1*s0*s1*s2*s3*s0*s1*s0*s1*s0*s2*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s3*s0*s1*s0*s2*s3*s1*s0*s1*s2*s3*s0*s1*s0*s1*s0*s2*s1 >;

References

None.

to this polytope.