Part of the Atlas of Small Regular Polytopes

Polytope of Type {44,6}

Atlas Canonical Name {44,6}*528b

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Overview

Group
SmallGroup(528,160)
Rank
3
Schläfli Type
{44,6}
Vertices, edges, …
44, 132, 6
Order of s0s1s2
33
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

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

References

None.

to this polytope.

Twisty Puzzle