Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,6,8}

Atlas Canonical Name {6,6,8}*1152a

Overview

Group
SmallGroup(1152,155791)
Rank
4
Schläfli Type
{6,6,8}
Vertices, edges, …
6, 36, 48, 16
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

8-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=<(s1*s2)^2*(s3*s2)^2*s1*s2*s3> of order 2

8 facets

6 vertex figures

Representations

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

References

None.

to this polytope.