Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,4,3}

Atlas Canonical Name {12,4,3}*1152

Overview

Group
SmallGroup(1152,155790)
Rank
4
Schläfli Type
{12,4,3}
Vertices, edges, …
24, 96, 24, 6
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

6-fold

12-fold

16-fold

24-fold

32-fold

48-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=<(s0*s1*s2*s1)^2> of order 2

6 facets

12 vertex figures

P/N, where N=<(s1*s2)^2, s0*s1*s2*s1*s0*s2> of order 4

4 facets

12 vertex figures

  • 12 of 2-fold non-regular quotient of {4,3}*48

Representations

Permutation Representation (GAP) 
s0 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,33)(18,34)(19,35)(20,36)(21,38)(22,37)(23,40)(24,39)(25,43)(26,44)(27,41)(28,42)(29,48)(30,47)(31,46)(32,45);;
s1 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,17)(10,18)(11,19)(12,20)(13,21)(14,22)(15,23)(16,24)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48);;
s2 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47);;
s3 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s3*s2*s3*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(48)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,33)(18,34)(19,35)(20,36)(21,38)(22,37)(23,40)(24,39)(25,43)(26,44)(27,41)(28,42)(29,48)(30,47)(31,46)(32,45);
s1 := Sym(48)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,17)(10,18)(11,19)(12,20)(13,21)(14,22)(15,23)(16,24)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48);
s2 := Sym(48)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47);
s3 := Sym(48)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44);
poly := sub<Sym(48)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s3*s2*s3*s0*s1 >;

References

None.

to this polytope.