Part of the Atlas of Small Regular Polytopes

Polytope of Type {60,6}

Atlas Canonical Name {60,6}*720d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(720,794)
Rank
3
Schläfli Type
{60,6}
Vertices, edges, …
60, 180, 6
Order of s0s1s2
15
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

15-fold

30-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle