Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,20}

Atlas Canonical Name {4,6,20}*960c

Overview

Group
SmallGroup(960,11373)
Rank
4
Schläfli Type
{4,6,20}
Vertices, edges, …
4, 12, 60, 20
Order of s0s1s2s3
15
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

10-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.