Overview
- Group
- SmallGroup(256,5298)
- Rank
- 3
- Schläfli Type
- {8,16}
- Vertices, edges, …
- 8, 64, 16
- Order of s0s1s2
- 16
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
32-fold
Covers minimal covers in bold
2-fold
3-fold
5-fold
7-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,41)(10,42)(11,44)(12,43)(13,47)(14,48)(15,45)(16,46)(17,49)(18,50)(19,52)(20,51)(21,55)(22,56)(23,53)(24,54)(25,58)(26,57)(27,59)(28,60)(29,64)(30,63)(31,62)(32,61);; s1 := ( 3, 4)( 5, 7)( 6, 8)(11,12)(13,15)(14,16)(17,21)(18,22)(19,24)(20,23)(25,30)(26,29)(27,31)(28,32)(33,41)(34,42)(35,44)(36,43)(37,47)(38,48)(39,45)(40,46)(49,63)(50,64)(51,61)(52,62)(53,59)(54,60)(55,57)(56,58);; s2 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,23)( 6,24)( 7,21)( 8,22)( 9,27)(10,28)(11,25)(12,26)(13,30)(14,29)(15,31)(16,32)(33,49)(34,50)(35,52)(36,51)(37,55)(38,56)(39,53)(40,54)(41,59)(42,60)(43,57)(44,58)(45,62)(46,61)(47,63)(48,64);; 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, s2*s0*s1*s2*s1*s2*s0*s1*s2*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(64)!( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,41)(10,42)(11,44)(12,43)(13,47)(14,48)(15,45)(16,46)(17,49)(18,50)(19,52)(20,51)(21,55)(22,56)(23,53)(24,54)(25,58)(26,57)(27,59)(28,60)(29,64)(30,63)(31,62)(32,61); s1 := Sym(64)!( 3, 4)( 5, 7)( 6, 8)(11,12)(13,15)(14,16)(17,21)(18,22)(19,24)(20,23)(25,30)(26,29)(27,31)(28,32)(33,41)(34,42)(35,44)(36,43)(37,47)(38,48)(39,45)(40,46)(49,63)(50,64)(51,61)(52,62)(53,59)(54,60)(55,57)(56,58); s2 := Sym(64)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,23)( 6,24)( 7,21)( 8,22)( 9,27)(10,28)(11,25)(12,26)(13,30)(14,29)(15,31)(16,32)(33,49)(34,50)(35,52)(36,51)(37,55)(38,56)(39,53)(40,54)(41,59)(42,60)(43,57)(44,58)(45,62)(46,61)(47,63)(48,64); poly := sub<Sym(64)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.