Overview
- Group
- SmallGroup(1512,486)
- Rank
- 3
- Schläfli Type
- {42,6}
- Vertices, edges, …
- 126, 378, 18
- Order of s0s1s2
- 42
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
Quotients maximal quotients in bold
3-fold
7-fold
9-fold
14-fold
21-fold
27-fold
42-fold
54-fold
63-fold
126-fold
189-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4,19)( 5,21)( 6,20)( 7,16)( 8,18)( 9,17)(10,13)(11,15)(12,14)(23,24)(25,40)(26,42)(27,41)(28,37)(29,39)(30,38)(31,34)(32,36)(33,35)(44,45)(46,61)(47,63)(48,62)(49,58)(50,60)(51,59)(52,55)(53,57)(54,56);; s1 := ( 1, 4)( 2, 5)( 3, 6)( 7,19)( 8,20)( 9,21)(10,16)(11,17)(12,18)(22,48)(23,46)(24,47)(25,45)(26,43)(27,44)(28,63)(29,61)(30,62)(31,60)(32,58)(33,59)(34,57)(35,55)(36,56)(37,54)(38,52)(39,53)(40,51)(41,49)(42,50);; s2 := ( 1,22)( 2,23)( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42);; 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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(63)!( 2, 3)( 4,19)( 5,21)( 6,20)( 7,16)( 8,18)( 9,17)(10,13)(11,15)(12,14)(23,24)(25,40)(26,42)(27,41)(28,37)(29,39)(30,38)(31,34)(32,36)(33,35)(44,45)(46,61)(47,63)(48,62)(49,58)(50,60)(51,59)(52,55)(53,57)(54,56); s1 := Sym(63)!( 1, 4)( 2, 5)( 3, 6)( 7,19)( 8,20)( 9,21)(10,16)(11,17)(12,18)(22,48)(23,46)(24,47)(25,45)(26,43)(27,44)(28,63)(29,61)(30,62)(31,60)(32,58)(33,59)(34,57)(35,55)(36,56)(37,54)(38,52)(39,53)(40,51)(41,49)(42,50); s2 := Sym(63)!( 1,22)( 2,23)( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42); poly := sub<Sym(63)|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*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.