Overview
- Group
- SmallGroup(504,169)
- Rank
- 3
- Schläfli Type
- {6,28}
- Vertices, edges, …
- 9, 126, 42
- Order of s0s1s2
- 28
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
7-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 := ( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56);; s1 := ( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(16,21)(17,20)(18,19)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,42)(38,41)(39,40)(43,50)(44,56)(45,55)(46,54)(47,53)(48,52)(49,51)(58,63)(59,62)(60,61);; s2 := ( 1, 2)( 3, 7)( 4, 6)( 8,23)( 9,22)(10,28)(11,27)(12,26)(13,25)(14,24)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(29,30)(31,35)(32,34)(36,51)(37,50)(38,56)(39,55)(40,54)(41,53)(42,52)(57,58)(59,63)(60,62);; 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*s1*s0*s1*s0*s2*s1*s0*s2*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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(63)!( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,57)(30,58)(31,59)(32,60)(33,61)(34,62)(35,63)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56); s1 := Sym(63)!( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(16,21)(17,20)(18,19)(22,29)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,42)(38,41)(39,40)(43,50)(44,56)(45,55)(46,54)(47,53)(48,52)(49,51)(58,63)(59,62)(60,61); s2 := Sym(63)!( 1, 2)( 3, 7)( 4, 6)( 8,23)( 9,22)(10,28)(11,27)(12,26)(13,25)(14,24)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(29,30)(31,35)(32,34)(36,51)(37,50)(38,56)(39,55)(40,54)(41,53)(42,52)(57,58)(59,63)(60,62); 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*s1*s0*s1*s0*s2*s1*s0*s2*s1, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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.