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  2. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    The surface area of a regular tetrahedron is four times the area of an equilateral triangle: [6] = =. The height of a regular tetrahedron is 6 3 a {\textstyle {\frac {\sqrt {6}}{3}}a} . [ 7 ] The volume of a regular tetrahedron can be ascertained similarly as the other pyramids, one-third of the base and its height.

  3. Triangulation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Triangulation_(geometry)

    In cartography, a triangulated irregular network is a point set triangulation of a set of two-dimensional points together with elevations for each point. Lifting each point from the plane to its elevated height lifts the triangles of the triangulation into three-dimensional surfaces, which form an approximation of a three-dimensional landform.

  4. Tesseract - Wikipedia

    en.wikipedia.org/wiki/Tesseract

    In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1] Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles.

  5. Steradian - Wikipedia

    en.wikipedia.org/wiki/Steradian

    A steradian can be defined as the solid angle subtended at the centre of a unit sphere by a unit area (of any shape) on its surface. For a general sphere of radius r, any portion of its surface with area A = r 2 subtends one steradian at its centre. [3] A solid angle in the form of a circular cone is related to the area it cuts out of a sphere:

  6. Surface triangulation - Wikipedia

    en.wikipedia.org/wiki/Surface_triangulation

    [3] [4] [5] The triangulation starts with a triangulated hexagon at a starting point. This hexagon is then surrounded by new triangles, following given rules, until the surface of consideration is triangulated. If the surface consists of several components, the algorithm has to be started several times using suitable starting points.

  7. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    There are only three shapes that can form such regular tessellations: the equilateral triangle, square and the regular hexagon. Any one of these three shapes can be duplicated infinitely to fill a plane with no gaps. [6] Many other types of tessellation are possible under different constraints.

  8. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides that are straight relative to the surface . A curvilinear triangle is a shape with three curved sides, for instance, a circular triangle with circular-arc sides. This article is about straight-sided triangles in Euclidean geometry, except where ...

  9. Surface area - Wikipedia

    en.wikipedia.org/wiki/Surface_area

    A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...

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