Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,6}

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

Overview

Group
SmallGroup(1152,155790)
Rank
4
Schläfli Type
{4,6,6}
Vertices, edges, …
16, 48, 72, 6
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

12-fold

24-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*s0)^2*(s1*s2)^2*s1> of order 2

6 facets

8 vertex figures

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

6 facets

8 vertex figures

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

6 facets

4 vertex figures

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4

6 facets

4 vertex figures

Representations

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

References

None.

to this polytope.