Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,12,3}

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

Overview

Group
SmallGroup(1440,4612)
Rank
4
Schläfli Type
{3,12,3}
Vertices, edges, …
15, 120, 120, 5
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 := ( 1,15)( 2,16)( 3,13)( 4,14)( 7, 8)( 9,28)(10,25)(11,26)(12,27)(17,29)(18,30)(19,32)(20,31)(21,22)(33,36)(37,40)(38,39)(42,43);;
s1 := ( 3, 4)( 5,11)( 6,12)( 7,10)( 8, 9)(13,22)(14,21)(15,24)(16,23)(17,39)(18,37)(19,40)(20,38)(25,28)(29,31)(30,32)(33,36)(41,42);;
s2 := ( 1, 3)( 2, 4)( 5, 6)( 9,30)(10,29)(11,31)(12,32)(13,15)(14,16)(17,25)(18,28)(19,27)(20,26)(21,36)(22,33)(23,35)(24,34)(37,40)(38,39);;
s3 := ( 1,27)( 2,26)( 3,28)( 4,25)( 5,23)( 6,24)( 7,21)( 8,22)( 9,13)(10,14)(11,16)(12,15)(17,20)(18,19)(29,31)(30,32)(34,35)(37,40)(38,39);;
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, s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
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)!( 1,15)( 2,16)( 3,13)( 4,14)( 7, 8)( 9,28)(10,25)(11,26)(12,27)(17,29)(18,30)(19,32)(20,31)(21,22)(33,36)(37,40)(38,39)(42,43);
s1 := Sym(43)!( 3, 4)( 5,11)( 6,12)( 7,10)( 8, 9)(13,22)(14,21)(15,24)(16,23)(17,39)(18,37)(19,40)(20,38)(25,28)(29,31)(30,32)(33,36)(41,42);
s2 := Sym(43)!( 1, 3)( 2, 4)( 5, 6)( 9,30)(10,29)(11,31)(12,32)(13,15)(14,16)(17,25)(18,28)(19,27)(20,26)(21,36)(22,33)(23,35)(24,34)(37,40)(38,39);
s3 := Sym(43)!( 1,27)( 2,26)( 3,28)( 4,25)( 5,23)( 6,24)( 7,21)( 8,22)( 9,13)(10,14)(11,16)(12,15)(17,20)(18,19)(29,31)(30,32)(34,35)(37,40)(38,39);
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, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2, 
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.