Overview
- Group
- SmallGroup(336,198)
- Rank
- 3
- Schläfli Type
- {4,42}
- Vertices, edges, …
- 4, 84, 42
- Order of s0s1s2
- 84
- Order of s0s1s2s1
- 2
- Also known as
- {4,42|2}. if this polytope has another name.
Special Properties
- 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
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84);; s1 := ( 1,43)( 2,49)( 3,48)( 4,47)( 5,46)( 6,45)( 7,44)( 8,57)( 9,63)(10,62)(11,61)(12,60)(13,59)(14,58)(15,50)(16,56)(17,55)(18,54)(19,53)(20,52)(21,51)(22,64)(23,70)(24,69)(25,68)(26,67)(27,66)(28,65)(29,78)(30,84)(31,83)(32,82)(33,81)(34,80)(35,79)(36,71)(37,77)(38,76)(39,75)(40,74)(41,73)(42,72);; s2 := ( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,30)(23,29)(24,35)(25,34)(26,33)(27,32)(28,31)(36,37)(38,42)(39,41)(43,51)(44,50)(45,56)(46,55)(47,54)(48,53)(49,52)(57,58)(59,63)(60,62)(64,72)(65,71)(66,77)(67,76)(68,75)(69,74)(70,73)(78,79)(80,84)(81,83);; 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*s2*s1*s0*s1*s2*s1, 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(84)!(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84); s1 := Sym(84)!( 1,43)( 2,49)( 3,48)( 4,47)( 5,46)( 6,45)( 7,44)( 8,57)( 9,63)(10,62)(11,61)(12,60)(13,59)(14,58)(15,50)(16,56)(17,55)(18,54)(19,53)(20,52)(21,51)(22,64)(23,70)(24,69)(25,68)(26,67)(27,66)(28,65)(29,78)(30,84)(31,83)(32,82)(33,81)(34,80)(35,79)(36,71)(37,77)(38,76)(39,75)(40,74)(41,73)(42,72); s2 := Sym(84)!( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,30)(23,29)(24,35)(25,34)(26,33)(27,32)(28,31)(36,37)(38,42)(39,41)(43,51)(44,50)(45,56)(46,55)(47,54)(48,53)(49,52)(57,58)(59,63)(60,62)(64,72)(65,71)(66,77)(67,76)(68,75)(69,74)(70,73)(78,79)(80,84)(81,83); poly := sub<Sym(84)|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*s2*s1*s0*s1*s2*s1, 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 >;
References
None.
to this polytope.