Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,12}

Atlas Canonical Name {12,12}*1944d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1944,2324)
Rank
3
Schläfli Type
{12,12}
Vertices, edges, …
81, 486, 81
Order of s0s1s2
6
Order of s0s1s2s1
3
Also known as
if this polytope has a name.

Special Properties

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

Quotients maximal quotients in bold

27-fold

Covers minimal covers in bold

None in this atlas.

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*(s2*s1)^3*s0*(s2*s1)^2*s2> of order 3

27 facets

27 vertex figures

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

27 facets

27 vertex figures

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

27 facets

27 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 4, 5)( 7, 9)(10,19)(11,21)(12,20)(13,23)(14,22)(15,24)(16,27)(17,26)(18,25);;
s1 := ( 1,10)( 2,17)( 3,15)( 4,16)( 5,14)( 6,12)( 7,13)( 8,11)( 9,18)(20,26)(21,24)(22,25);;
s2 := ( 4, 9)( 5, 7)( 6, 8)(10,21)(11,19)(12,20)(13,26)(14,27)(15,25)(16,22)(17,23)(18,24);;
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*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(27)!( 2, 3)( 4, 5)( 7, 9)(10,19)(11,21)(12,20)(13,23)(14,22)(15,24)(16,27)(17,26)(18,25);
s1 := Sym(27)!( 1,10)( 2,17)( 3,15)( 4,16)( 5,14)( 6,12)( 7,13)( 8,11)( 9,18)(20,26)(21,24)(22,25);
s2 := Sym(27)!( 4, 9)( 5, 7)( 6, 8)(10,21)(11,19)(12,20)(13,26)(14,27)(15,25)(16,22)(17,23)(18,24);
poly := sub<Sym(27)|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*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.

Twisty Puzzle