Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,12,3}

Atlas Canonical Name {12,12,3}*1920

Overview

Group
SmallGroup(1920,240844)
Rank
4
Schläfli Type
{12,12,3}
Vertices, edges, …
20, 160, 40, 5
Order of s0s1s2s3
20
Order of s0s1s2s3s2s1
12
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 1,37)( 2,36)( 3,39)( 4,33)( 5,32)( 6,29)( 7,25)( 8,40)( 9,19)(10,16)(12,23)(14,21)(15,38)(17,35)(18,26)(22,24)(31,34)(42,44);;
s1 := ( 1,23)( 2,21)( 3,33)( 4,32)( 6,17)( 7,34)( 8,22)( 9,36)(11,15)(12,13)(18,38)(20,26)(24,35)(25,40)(27,28)(29,31)(30,37)(41,44)(42,43);;
s2 := ( 1,39)( 3,37)( 4,10)( 5,23)( 6,18)( 7,25)( 8,15)( 9,22)(11,20)(12,32)(13,28)(14,34)(16,33)(17,35)(19,24)(21,31)(26,29)(27,30)(38,40);;
s3 := ( 1,18)( 2, 4)( 3, 9)( 5,14)( 6,24)( 7,25)( 8,31)(11,13)(12,15)(17,35)(19,39)(20,30)(21,32)(22,29)(23,38)(26,37)(27,28)(33,36)(34,40);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(44)!( 1,37)( 2,36)( 3,39)( 4,33)( 5,32)( 6,29)( 7,25)( 8,40)( 9,19)(10,16)(12,23)(14,21)(15,38)(17,35)(18,26)(22,24)(31,34)(42,44);
s1 := Sym(44)!( 1,23)( 2,21)( 3,33)( 4,32)( 6,17)( 7,34)( 8,22)( 9,36)(11,15)(12,13)(18,38)(20,26)(24,35)(25,40)(27,28)(29,31)(30,37)(41,44)(42,43);
s2 := Sym(44)!( 1,39)( 3,37)( 4,10)( 5,23)( 6,18)( 7,25)( 8,15)( 9,22)(11,20)(12,32)(13,28)(14,34)(16,33)(17,35)(19,24)(21,31)(26,29)(27,30)(38,40);
s3 := Sym(44)!( 1,18)( 2, 4)( 3, 9)( 5,14)( 6,24)( 7,25)( 8,31)(11,13)(12,15)(17,35)(19,39)(20,30)(21,32)(22,29)(23,38)(26,37)(27,28)(33,36)(34,40);
poly := sub<Sym(44)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.