Part of the Atlas of Small Regular Polytopes

Polytope of Type {66,6}

Atlas Canonical Name {66,6}*1188

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1188,41)
Rank
3
Schläfli Type
{66,6}
Vertices, edges, …
99, 297, 9
Order of s0s1s2
33
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

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle