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  2. Archimedean solid - Wikipedia

    en.wikipedia.org/wiki/Archimedean_solid

    32 triangles 6 squares 60 24 O Icosidodecahedron: 3.5.3.5: 20 triangles 12 pentagons: 60 30 I h: Truncated dodecahedron: 3.10.10: 20 triangles 12 decagons: 90 60 I h: Truncated icosahedron: 5.6.6: 12 pentagons 20 hexagons 90 60 I h: Rhombicosidodecahedron: 3.4.5.4: 20 triangles 30 squares 12 pentagons 120 60 I h: Truncated icosidodecahedron: 4. ...

  3. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    If D = 1, a unique solution exists: γ = 90°, i.e., the triangle is right-angled. If D < 1 two alternatives are possible. If b ≥ c, then β ≥ γ (the larger side corresponds to a larger angle). Since no triangle can have two obtuse angles, γ is an acute angle and the solution γ = arcsin D is unique.

  4. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Twelve key lengths of a triangle are the three side lengths, the three altitudes, the three medians, and the three angle bisectors. Together with the three angles, these give 95 distinct combinations, 63 of which give rise to a constructible triangle, 30 of which do not, and two of which are underdefined. [13]: pp. 201–203

  5. Modern triangle geometry - Wikipedia

    en.wikipedia.org/wiki/Modern_triangle_geometry

    Here is a definition of triangle geometry from 1887: "Being given a point M in the plane of the triangle, we can always find, in an infinity of manners, a second point M' that corresponds to the first one according to an imagined geometrical law; these two points have between them geometrical relations whose simplicity depends on the more or ...

  6. Fermat point - Wikipedia

    en.wikipedia.org/wiki/Fermat_point

    Fig 1. Construction of the first isogonic center, X(13). When no angle of the triangle exceeds 120°, this point is the Fermat point. In Euclidean geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible [1] or ...

  7. Triangle center - Wikipedia

    en.wikipedia.org/wiki/Triangle_center

    In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid , circumcenter , incenter and orthocenter were familiar to the ancient Greeks , and can be obtained by simple constructions .

  8. Euler line - Wikipedia

    en.wikipedia.org/wiki/Euler_line

    In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.

  9. Barycentric coordinate system - Wikipedia

    en.wikipedia.org/wiki/Barycentric_coordinate_system

    Barycentric coordinates (,,) on an equilateral triangle and on a right triangle. A 3-simplex, with barycentric subdivisions of 1-faces (edges) 2-faces (triangles) and 3-faces (body). In geometry , a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points ...