Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,6,20}

Atlas Canonical Name {6,6,20}*1440d

Overview

Group
SmallGroup(1440,5871)
Rank
4
Schläfli Type
{6,6,20}
Vertices, edges, …
6, 18, 60, 20
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

10-fold

15-fold

30-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);;
s1 := ( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)(10,30)(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)(43,44)(47,48)(51,52)(55,56)(59,60);;
s2 := ( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)(21,41)(22,44)(23,43)(24,42)(25,57)(26,60)(27,59)(28,58)(29,53)(30,56)(31,55)(32,54)(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)(40,46);;
s3 := ( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,18)(10,17)(11,20)(12,19)(13,14)(15,16)(21,26)(22,25)(23,28)(24,27)(29,38)(30,37)(31,40)(32,39)(33,34)(35,36)(41,46)(42,45)(43,48)(44,47)(49,58)(50,57)(51,60)(52,59)(53,54)(55,56);;
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*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(60)!(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);
s1 := Sym(60)!( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)(10,30)(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)(43,44)(47,48)(51,52)(55,56)(59,60);
s2 := Sym(60)!( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)(21,41)(22,44)(23,43)(24,42)(25,57)(26,60)(27,59)(28,58)(29,53)(30,56)(31,55)(32,54)(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)(40,46);
s3 := Sym(60)!( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,18)(10,17)(11,20)(12,19)(13,14)(15,16)(21,26)(22,25)(23,28)(24,27)(29,38)(30,37)(31,40)(32,39)(33,34)(35,36)(41,46)(42,45)(43,48)(44,47)(49,58)(50,57)(51,60)(52,59)(53,54)(55,56);
poly := sub<Sym(60)|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*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.