Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,6,3,4}

Atlas Canonical Name {10,6,3,4}*1440

Overview

Group
SmallGroup(1440,5871)
Rank
5
Schläfli Type
{10,6,3,4}
Vertices, edges, …
10, 30, 9, 6, 4
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
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

6-fold

15-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)(25,37)(26,38)(27,39)(28,40)(29,33)(30,34)(31,35)(32,36)(45,57)(46,58)(47,59)(48,60)(49,53)(50,54)(51,55)(52,56);;
s1 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,17)(10,18)(11,19)(12,20)(21,45)(22,46)(23,47)(24,48)(25,41)(26,42)(27,43)(28,44)(29,57)(30,58)(31,59)(32,60)(33,53)(34,54)(35,55)(36,56)(37,49)(38,50)(39,51)(40,52);;
s2 := ( 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);;
s3 := ( 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);;
s4 := ( 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,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, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)(25,37)(26,38)(27,39)(28,40)(29,33)(30,34)(31,35)(32,36)(45,57)(46,58)(47,59)(48,60)(49,53)(50,54)(51,55)(52,56);
s1 := Sym(60)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,17)(10,18)(11,19)(12,20)(21,45)(22,46)(23,47)(24,48)(25,41)(26,42)(27,43)(28,44)(29,57)(30,58)(31,59)(32,60)(33,53)(34,54)(35,55)(36,56)(37,49)(38,50)(39,51)(40,52);
s2 := 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);
s3 := 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);
s4 := 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,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, s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.