Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,12}

Atlas Canonical Name {12,12}*384a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(384,17873)
Rank
3
Schläfli Type
{12,12}
Vertices, edges, …
16, 96, 16
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

12-fold

16-fold

24-fold

48-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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