Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,3,4,6}

Atlas Canonical Name {3,3,4,6}*1152

Overview

Group
SmallGroup(1152,155790)
Rank
5
Schläfli Type
{3,3,4,6}
Vertices, edges, …
4, 12, 16, 24, 6
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
2
Also known as
{{3,3,4}4,{{3,4},{4,6|2}}}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

8-fold

12-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=<(s2*s3)^2> of order 2

6 facets

4 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 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);;
s1 := ( 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);;
s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,21)(18,22)(19,24)(20,23)(27,28)(31,32)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48);;
s3 := ( 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);;
s4 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s0*s2*s3*s1*s2*s3*s1*s2*s3*s0*s1*s2*s3*s0*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := 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);
s1 := 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);
s2 := Sym(48)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(15,16)(17,21)(18,22)(19,24)(20,23)(27,28)(31,32)(33,37)(34,38)(35,40)(36,39)(43,44)(47,48);
s3 := 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);
s4 := Sym(48)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32);
poly := sub<Sym(48)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s0*s2*s3*s1*s2*s3*s1*s2*s3*s0*s1*s2*s3*s0*s2 >;

References

None.

to this polytope.