Overview
- Group
- SmallGroup(756,98)
- Rank
- 3
- Schläfli Type
- {21,6}
- Vertices, edges, …
- 63, 189, 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
Quotients maximal quotients in bold
3-fold
7-fold
9-fold
21-fold
27-fold
63-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 4,19)( 5,20)( 6,21)( 7,16)( 8,17)( 9,18)(10,13)(11,14)(12,15)(22,43)(23,44)(24,45)(25,61)(26,62)(27,63)(28,58)(29,59)(30,60)(31,55)(32,56)(33,57)(34,52)(35,53)(36,54)(37,49)(38,50)(39,51)(40,46)(41,47)(42,48);; s1 := ( 1,26)( 2,27)( 3,25)( 4,23)( 5,24)( 6,22)( 7,41)( 8,42)( 9,40)(10,38)(11,39)(12,37)(13,35)(14,36)(15,34)(16,32)(17,33)(18,31)(19,29)(20,30)(21,28)(43,46)(44,47)(45,48)(49,61)(50,62)(51,63)(52,58)(53,59)(54,60);; s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0,
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(63)!( 4,19)( 5,20)( 6,21)( 7,16)( 8,17)( 9,18)(10,13)(11,14)(12,15)(22,43)(23,44)(24,45)(25,61)(26,62)(27,63)(28,58)(29,59)(30,60)(31,55)(32,56)(33,57)(34,52)(35,53)(36,54)(37,49)(38,50)(39,51)(40,46)(41,47)(42,48); s1 := Sym(63)!( 1,26)( 2,27)( 3,25)( 4,23)( 5,24)( 6,22)( 7,41)( 8,42)( 9,40)(10,38)(11,39)(12,37)(13,35)(14,36)(15,34)(16,32)(17,33)(18,31)(19,29)(20,30)(21,28)(43,46)(44,47)(45,48)(49,61)(50,62)(51,63)(52,58)(53,59)(54,60); s2 := Sym(63)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63); 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, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, 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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.