Part of the Atlas of Small Regular Polytopes

Polytope of Type {92,6}

Atlas Canonical Name {92,6}*1104b

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Overview

Group
SmallGroup(1104,160)
Rank
3
Schläfli Type
{92,6}
Vertices, edges, …
92, 276, 6
Order of s0s1s2
69
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

23-fold

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

References

None.

to this polytope.

Twisty Puzzle