Overview
- Group
- SmallGroup(336,196)
- Rank
- 3
- Schläfli Type
- {2,84}
- Vertices, edges, …
- 2, 84, 84
- Order of s0s1s2
- 84
- Order of s0s1s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
7-fold
12-fold
14-fold
21-fold
28-fold
42-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(45,66)(46,72)(47,71)(48,70)(49,69)(50,68)(51,67)(52,80)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,73)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74);; s2 := ( 3,53)( 4,52)( 5,58)( 6,57)( 7,56)( 8,55)( 9,54)(10,46)(11,45)(12,51)(13,50)(14,49)(15,48)(16,47)(17,60)(18,59)(19,65)(20,64)(21,63)(22,62)(23,61)(24,74)(25,73)(26,79)(27,78)(28,77)(29,76)(30,75)(31,67)(32,66)(33,72)(34,71)(35,70)(36,69)(37,68)(38,81)(39,80)(40,86)(41,85)(42,84)(43,83)(44,82);; 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*s1*s0*s1, s0*s2*s0*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*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*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*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*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(86)!(1,2); s1 := Sym(86)!( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(45,66)(46,72)(47,71)(48,70)(49,69)(50,68)(51,67)(52,80)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,73)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74); s2 := Sym(86)!( 3,53)( 4,52)( 5,58)( 6,57)( 7,56)( 8,55)( 9,54)(10,46)(11,45)(12,51)(13,50)(14,49)(15,48)(16,47)(17,60)(18,59)(19,65)(20,64)(21,63)(22,62)(23,61)(24,74)(25,73)(26,79)(27,78)(28,77)(29,76)(30,75)(31,67)(32,66)(33,72)(34,71)(35,70)(36,69)(37,68)(38,81)(39,80)(40,86)(41,85)(42,84)(43,83)(44,82); poly := sub<Sym(86)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*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*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*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*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*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 >;