Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,12,3}

Atlas Canonical Name {3,12,3}*1440a

Overview

Group
SmallGroup(1440,4612)
Rank
4
Schläfli Type
{3,12,3}
Vertices, edges, …
5, 120, 120, 15
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
12
Also known as
if this polytope has a name.

Special Properties

  • Orientable

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

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

References

None.

to this polytope.