Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,6}

Atlas Canonical Name {8,6}*384d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(384,17949)
Rank
3
Schläfli Type
{8,6}
Vertices, edges, …
32, 96, 24
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=<(s0*s1)^4> of order 2

16 facets

16 vertex figures

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

12 facets

16 vertex figures

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

12 facets

16 vertex figures

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

8 facets

8 vertex figures

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

12 facets

8 vertex figures

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

8 facets

8 vertex figures

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

8 facets

8 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle