Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
tessellations of the sphere, plane, and hyperbolic plane
|
| gptkbp:definedIn |
groups generated by reflections in the sides of a triangle
|
| gptkbp:example |
gptkb:(2,3,4)-triangle_group
gptkb:(2,3,5)-triangle_group gptkb:(2,3,6)-triangle_group gptkb:(2,3,7)-triangle_group |
| gptkbp:field |
gptkb:geometry
group theory |
| gptkbp:finite_for |
(l, m, n) with 1/l + 1/m + 1/n > 1
|
| gptkbp:hasSpecialCase |
modular group
|
| https://www.w3.org/2000/01/rdf-schema#label |
triangle groups
|
| gptkbp:infinite_for |
(l, m, n) with 1/l + 1/m + 1/n ≤ 1
|
| gptkbp:introduced |
gptkb:Felix_Klein
|
| gptkbp:notation |
gptkb:(l,_m,_n)-triangle_group
|
| gptkbp:presentedBy |
⟨x, y, z | x^l = y^m = z^n = xyz = 1⟩
|
| gptkbp:relatedTo |
gptkb:Coxeter_groups
gptkb:Fuchsian_groups symmetry groups of tilings |
| gptkbp:used_in |
gptkb:monodromy_groups
classification of regular polyhedra |
| gptkbp:bfsParent |
gptkb:Hurwitz_surfaces
gptkb:Fuchsian_groups |
| gptkbp:bfsLayer |
6
|