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  2. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    The characteristic tetrahedron of the cube is an example of a ... formula for the volume of a tetrahedron ... 2, x 3 can be formulated as matrix-vector ...

  3. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space

  4. Simplex - Wikipedia

    en.wikipedia.org/wiki/Simplex

    In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment,

  5. Barycentric coordinate system - Wikipedia

    en.wikipedia.org/wiki/Barycentric_coordinate_system

    As the direction of this vector ... One may prove these ratio formulas ... where V is the volume of the tetrahedron. Examples of special points. In the ...

  6. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    For example a tetrahedron is a polyhedron with four ... (See Volume § Volume formulas for a list that includes many of these ... is the unit vector perpendicular ...

  7. Multiple integral - Wikipedia

    en.wikipedia.org/wiki/Multiple_integral

    Example of a domain transformation from cartesian to polar. Example 2c. The domain is D = {x 2 + y 2 ≤ 4}, that is a circumference of radius 2; it's evident that the covered angle is the circle angle, so φ varies from 0 to 2 π, while the crown radius varies from 0 to 2 (the crown with the inside radius null is just a circle). Example 2d.

  8. Reeve tetrahedra - Wikipedia

    en.wikipedia.org/wiki/Reeve_tetrahedra

    All vertices of a Reeve tetrahedron are lattice points (points whose coordinates are all integers). No other lattice points lie on the surface or in the interior of the tetrahedron. The volume of the Reeve tetrahedron with vertex (1, 1, r) is r/6. In 1957 Reeve used this tetrahedron to show that there exist tetrahedra with four lattice points ...

  9. Ideal polyhedron - Wikipedia

    en.wikipedia.org/wiki/Ideal_polyhedron

    The volume of an ideal tetrahedron can be expressed in terms of the Clausen function or Lobachevsky function of its dihedral angles, and the volume of an arbitrary ideal polyhedron can then be found by partitioning it into tetrahedra and summing the volumes of the tetrahedra.