Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,6}

Atlas Canonical Name {8,6}*192b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(192,1481)
Rank
3
Schläfli Type
{8,6}
Vertices, edges, …
16, 48, 12
Order of s0s1s2
12
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

24-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle