Part of the Atlas of Small Regular Polytopes

Polytope of Type {30,6,4}

Atlas Canonical Name {30,6,4}*1440d

Overview

Group
SmallGroup(1440,5871)
Rank
4
Schläfli Type
{30,6,4}
Vertices, edges, …
30, 90, 12, 4
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 := ( 5,17)( 6,18)( 7,19)( 8,20)( 9,13)(10,14)(11,15)(12,16)(21,41)(22,42)(23,43)(24,44)(25,57)(26,58)(27,59)(28,60)(29,53)(30,54)(31,55)(32,56)(33,49)(34,50)(35,51)(36,52)(37,45)(38,46)(39,47)(40,48);;
s1 := ( 1,25)( 2,26)( 3,28)( 4,27)( 5,21)( 6,22)( 7,24)( 8,23)( 9,37)(10,38)(11,40)(12,39)(13,33)(14,34)(15,36)(16,35)(17,29)(18,30)(19,32)(20,31)(41,45)(42,46)(43,48)(44,47)(49,57)(50,58)(51,60)(52,59)(55,56);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(21,41)(22,44)(23,43)(24,42)(25,45)(26,48)(27,47)(28,46)(29,49)(30,52)(31,51)(32,50)(33,53)(34,56)(35,55)(36,54)(37,57)(38,60)(39,59)(40,58);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60);;
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*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(60)!( 5,17)( 6,18)( 7,19)( 8,20)( 9,13)(10,14)(11,15)(12,16)(21,41)(22,42)(23,43)(24,44)(25,57)(26,58)(27,59)(28,60)(29,53)(30,54)(31,55)(32,56)(33,49)(34,50)(35,51)(36,52)(37,45)(38,46)(39,47)(40,48);
s1 := Sym(60)!( 1,25)( 2,26)( 3,28)( 4,27)( 5,21)( 6,22)( 7,24)( 8,23)( 9,37)(10,38)(11,40)(12,39)(13,33)(14,34)(15,36)(16,35)(17,29)(18,30)(19,32)(20,31)(41,45)(42,46)(43,48)(44,47)(49,57)(50,58)(51,60)(52,59)(55,56);
s2 := Sym(60)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(21,41)(22,44)(23,43)(24,42)(25,45)(26,48)(27,47)(28,46)(29,49)(30,52)(31,51)(32,50)(33,53)(34,56)(35,55)(36,54)(37,57)(38,60)(39,59)(40,58);
s3 := Sym(60)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60);
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, 
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, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;

References

None.

to this polytope.