Part of the Atlas of Small Regular Polytopes

Polytope of Type {33,6}

Atlas Canonical Name {33,6}*528

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Overview

Group
SmallGroup(528,160)
Rank
3
Schläfli Type
{33,6}
Vertices, edges, …
44, 132, 8
Order of s0s1s2
44
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

11-fold

12-fold

22-fold

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

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