Overview
- Group
- SmallGroup(336,148)
- Rank
- 3
- Schläfli Type
- {12,14}
- Vertices, edges, …
- 12, 84, 14
- Order of s0s1s2
- 84
- Order of s0s1s2s1
- 2
- Also known as
- {12,14|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
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 := ( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,78)(51,79)(52,80)(53,81)(54,82)(55,83)(56,84)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77);; s1 := ( 1,50)( 2,56)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,57)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,71)(23,77)(24,76)(25,75)(26,74)(27,73)(28,72)(29,64)(30,70)(31,69)(32,68)(33,67)(34,66)(35,65)(36,78)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79);; s2 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)(10,14)(11,13)(15,16)(17,21)(18,20)(22,23)(24,28)(25,27)(29,30)(31,35)(32,34)(36,37)(38,42)(39,41)(43,44)(45,49)(46,48)(50,51)(52,56)(53,55)(57,58)(59,63)(60,62)(64,65)(66,70)(67,69)(71,72)(73,77)(74,76)(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*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,
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)!( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,64)(44,65)(45,66)(46,67)(47,68)(48,69)(49,70)(50,78)(51,79)(52,80)(53,81)(54,82)(55,83)(56,84)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77); s1 := Sym(84)!( 1,50)( 2,56)( 3,55)( 4,54)( 5,53)( 6,52)( 7,51)( 8,43)( 9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,57)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,71)(23,77)(24,76)(25,75)(26,74)(27,73)(28,72)(29,64)(30,70)(31,69)(32,68)(33,67)(34,66)(35,65)(36,78)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79); s2 := Sym(84)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)(10,14)(11,13)(15,16)(17,21)(18,20)(22,23)(24,28)(25,27)(29,30)(31,35)(32,34)(36,37)(38,42)(39,41)(43,44)(45,49)(46,48)(50,51)(52,56)(53,55)(57,58)(59,63)(60,62)(64,65)(66,70)(67,69)(71,72)(73,77)(74,76)(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*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, 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.