Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,8}

Atlas Canonical Name {6,8}*384d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(384,17949)
Rank
3
Schläfli Type
{6,8}
Vertices, edges, …
24, 96, 32
Order of s0s1s2
6
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

48-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<((s1*s0)^2*s1*s2)^2> of order 2

16 facets

16 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 2

16 facets

12 vertex figures

P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s1*s2> of order 2

16 facets

12 vertex figures

P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1, s0*(s1*s2)^2*(s1*s0)^2*s2*s1> of order 4

8 facets

8 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2> of order 4

8 facets

8 vertex figures

P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 4

8 facets

12 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, s1*s0*(s2*s1)^2*s0*s1*s2> of order 4

8 facets

8 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)(31,48)(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)(68,83)(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)(79,96)(80,95);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)(10,30)(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(34,35)(37,40)(41,48)(42,46)(43,47)(44,45)(49,65)(50,67)(51,66)(52,68)(53,72)(54,70)(55,71)(56,69)(57,80)(58,78)(59,79)(60,77)(61,76)(62,74)(63,75)(64,73)(82,83)(85,88)(89,96)(90,94)(91,95)(92,93);;
s2 := ( 1,61)( 2,62)( 3,63)( 4,64)( 5,57)( 6,58)( 7,59)( 8,60)( 9,53)(10,54)(11,55)(12,56)(13,49)(14,50)(15,51)(16,52)(17,77)(18,78)(19,79)(20,80)(21,73)(22,74)(23,75)(24,76)(25,69)(26,70)(27,71)(28,72)(29,65)(30,66)(31,67)(32,68)(33,93)(34,94)(35,95)(36,96)(37,89)(38,90)(39,91)(40,92)(41,85)(42,86)(43,87)(44,88)(45,81)(46,82)(47,83)(48,84);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(96)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)(31,48)(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)(68,83)(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)(79,96)(80,95);
s1 := Sym(96)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)(10,30)(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(34,35)(37,40)(41,48)(42,46)(43,47)(44,45)(49,65)(50,67)(51,66)(52,68)(53,72)(54,70)(55,71)(56,69)(57,80)(58,78)(59,79)(60,77)(61,76)(62,74)(63,75)(64,73)(82,83)(85,88)(89,96)(90,94)(91,95)(92,93);
s2 := Sym(96)!( 1,61)( 2,62)( 3,63)( 4,64)( 5,57)( 6,58)( 7,59)( 8,60)( 9,53)(10,54)(11,55)(12,56)(13,49)(14,50)(15,51)(16,52)(17,77)(18,78)(19,79)(20,80)(21,73)(22,74)(23,75)(24,76)(25,69)(26,70)(27,71)(28,72)(29,65)(30,66)(31,67)(32,68)(33,93)(34,94)(35,95)(36,96)(37,89)(38,90)(39,91)(40,92)(41,85)(42,86)(43,87)(44,88)(45,81)(46,82)(47,83)(48,84);
poly := sub<Sym(96)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle