Part of the Atlas of Small Regular Polytopes

Polytope of Type {42,6}

Atlas Canonical Name {42,6}*756

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(756,98)
Rank
3
Schläfli Type
{42,6}
Vertices, edges, …
63, 189, 9
Order of s0s1s2
21
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

7-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle