Overview
- Group
- SmallGroup(504,172)
- Rank
- 3
- Schläfli Type
- {42,6}
- Vertices, edges, …
- 42, 126, 6
- 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
- Flat
- Self-Petrie
Quotients maximal quotients in bold
3-fold
7-fold
9-fold
14-fold
18-fold
21-fold
42-fold
63-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(23,28)(24,27)(25,26)(29,36)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(44,49)(45,48)(46,47)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58);; s1 := ( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,58)(37,57)(38,63)(39,62)(40,61)(41,60)(42,59);; s2 := ( 1,22)( 2,23)( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,29)(16,30)(17,31)(18,32)(19,33)(20,34)(21,35)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(63)!( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(23,28)(24,27)(25,26)(29,36)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(44,49)(45,48)(46,47)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58); s1 := Sym(63)!( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,58)(37,57)(38,63)(39,62)(40,61)(41,60)(42,59); s2 := Sym(63)!( 1,22)( 2,23)( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,29)(16,30)(17,31)(18,32)(19,33)(20,34)(21,35)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62)(56,63); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.