Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,6}

Atlas Canonical Name {6,6}*384c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(384,17948)
Rank
3
Schläfli Type
{6,6}
Vertices, edges, …
32, 96, 32
Order of s0s1s2
4
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-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*s2)^2*s1)^2> of order 2

16 facets

16 vertex figures

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

16 facets

20 vertex figures

P/N, where N=<(s0*s1)^3> of order 2

20 facets

16 vertex figures

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

16 facets

16 vertex figures

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

16 facets

16 vertex figures

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

8 facets

8 vertex figures

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

8 facets

8 vertex figures

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

8 facets

8 vertex figures

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

8 facets

12 vertex figures

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

8 facets

8 vertex figures

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

8 facets

8 vertex figures

P/N, where N=<(s0*s1)^3, s0*s2*(s1*s0)^2*s1*s2> of order 4

12 facets

8 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle