Part of the Atlas of Small Regular Polytopes

Polytope of Type {14,6}

Atlas Canonical Name {14,6}*168

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(168,50)
Rank
3
Schläfli Type
{14,6}
Vertices, edges, …
14, 42, 6
Order of s0s1s2
42
Order of s0s1s2s1
2
Also known as
{14,6|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

6-fold

7-fold

14-fold

21-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(44,49)(45,48)(46,47)(51,56)(52,55)(53,54)(58,63)(59,62)(60,61)(65,70)(66,69)(67,68)(72,77)(73,76)(74,75)(79,84)(80,83)(81,82);;
s1 := ( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,58)( 9,57)(10,63)(11,62)(12,61)(13,60)(14,59)(15,51)(16,50)(17,56)(18,55)(19,54)(20,53)(21,52)(22,65)(23,64)(24,70)(25,69)(26,68)(27,67)(28,66)(29,79)(30,78)(31,84)(32,83)(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73);;
s2 := ( 1,71)( 2,72)( 3,73)( 4,74)( 5,75)( 6,76)( 7,77)( 8,64)( 9,65)(10,66)(11,67)(12,68)(13,69)(14,70)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(84)!( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(30,35)(31,34)(32,33)(37,42)(38,41)(39,40)(44,49)(45,48)(46,47)(51,56)(52,55)(53,54)(58,63)(59,62)(60,61)(65,70)(66,69)(67,68)(72,77)(73,76)(74,75)(79,84)(80,83)(81,82);
s1 := Sym(84)!( 1,44)( 2,43)( 3,49)( 4,48)( 5,47)( 6,46)( 7,45)( 8,58)( 9,57)(10,63)(11,62)(12,61)(13,60)(14,59)(15,51)(16,50)(17,56)(18,55)(19,54)(20,53)(21,52)(22,65)(23,64)(24,70)(25,69)(26,68)(27,67)(28,66)(29,79)(30,78)(31,84)(32,83)(33,82)(34,81)(35,80)(36,72)(37,71)(38,77)(39,76)(40,75)(41,74)(42,73);
s2 := Sym(84)!( 1,71)( 2,72)( 3,73)( 4,74)( 5,75)( 6,76)( 7,77)( 8,64)( 9,65)(10,66)(11,67)(12,68)(13,69)(14,70)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63);
poly := sub<Sym(84)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*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*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle