Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,44}

Atlas Canonical Name {6,44}*792

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Overview

Group
SmallGroup(792,113)
Rank
3
Schläfli Type
{6,44}
Vertices, edges, …
9, 198, 66
Order of s0s1s2
44
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

11-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (12,23)(13,24)(14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,89)(46,90)(47,91)(48,92)(49,93)(50,94)(51,95)(52,96)(53,97)(54,98)(55,99)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88);;
s1 := ( 1,34)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(13,22)(14,21)(15,20)(16,19)(17,18)(23,89)(24,99)(25,98)(26,97)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(45,78)(46,88)(47,87)(48,86)(49,85)(50,84)(51,83)(52,82)(53,81)(54,80)(55,79)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)(69,76)(70,75)(71,74)(72,73);;
s2 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,46)(35,45)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(56,57)(58,66)(59,65)(60,64)(61,63)(67,90)(68,89)(69,99)(70,98)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)(77,91)(78,79)(80,88)(81,87)(82,86)(83,85);;
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(99)!(12,23)(13,24)(14,25)(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,89)(46,90)(47,91)(48,92)(49,93)(50,94)(51,95)(52,96)(53,97)(54,98)(55,99)(56,78)(57,79)(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88);
s1 := Sym(99)!( 1,34)( 2,44)( 3,43)( 4,42)( 5,41)( 6,40)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(13,22)(14,21)(15,20)(16,19)(17,18)(23,89)(24,99)(25,98)(26,97)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(45,78)(46,88)(47,87)(48,86)(49,85)(50,84)(51,83)(52,82)(53,81)(54,80)(55,79)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)(69,76)(70,75)(71,74)(72,73);
s2 := Sym(99)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,46)(35,45)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(56,57)(58,66)(59,65)(60,64)(61,63)(67,90)(68,89)(69,99)(70,98)(71,97)(72,96)(73,95)(74,94)(75,93)(76,92)(77,91)(78,79)(80,88)(81,87)(82,86)(83,85);
poly := sub<Sym(99)|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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle