Overview
- Group
- SmallGroup(1512,486)
- Rank
- 3
- Schläfli Type
- {6,42}
- Vertices, edges, …
- 18, 378, 126
- 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
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 := (22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63);; s1 := ( 1,23)( 2,24)( 3,22)( 4,41)( 5,42)( 6,40)( 7,38)( 8,39)( 9,37)(10,35)(11,36)(12,34)(13,32)(14,33)(15,31)(16,29)(17,30)(18,28)(19,26)(20,27)(21,25)(46,61)(47,62)(48,63)(49,58)(50,59)(51,60)(52,55)(53,56)(54,57);; s2 := ( 1, 4)( 2, 6)( 3, 5)( 7,19)( 8,21)( 9,20)(10,16)(11,18)(12,17)(14,15)(22,25)(23,27)(24,26)(28,40)(29,42)(30,41)(31,37)(32,39)(33,38)(35,36)(43,46)(44,48)(45,47)(49,61)(50,63)(51,62)(52,58)(53,60)(54,59)(56,57);; 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*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(63)!(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63); s1 := Sym(63)!( 1,23)( 2,24)( 3,22)( 4,41)( 5,42)( 6,40)( 7,38)( 8,39)( 9,37)(10,35)(11,36)(12,34)(13,32)(14,33)(15,31)(16,29)(17,30)(18,28)(19,26)(20,27)(21,25)(46,61)(47,62)(48,63)(49,58)(50,59)(51,60)(52,55)(53,56)(54,57); s2 := Sym(63)!( 1, 4)( 2, 6)( 3, 5)( 7,19)( 8,21)( 9,20)(10,16)(11,18)(12,17)(14,15)(22,25)(23,27)(24,26)(28,40)(29,42)(30,41)(31,37)(32,39)(33,38)(35,36)(43,46)(44,48)(45,47)(49,61)(50,63)(51,62)(52,58)(53,60)(54,59)(56,57); 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*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.