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  2. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    The volume of a tetrahedron can be obtained in many ways. It can be given by using the formula of the pyramid's volume: =. where is the base' area and is the height from the base to the apex. This applies for each of the four choices of the base, so the distances from the apices to the opposite faces are inversely proportional to the areas of ...

  3. Simplex - Wikipedia

    en.wikipedia.org/wiki/Simplex

    Another common way of computing the volume of the simplex is via the Cayley–Menger determinant, which works even when the n-simplex's vertices are in a Euclidean space with more than n dimensions. [11] Without the 1/n! it is the formula for the volume of an n-parallelotope.

  4. 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

  5. Parallelepiped - Wikipedia

    en.wikipedia.org/wiki/Parallelepiped

    Corresponding tetrahedron. The volume of any tetrahedron that shares three converging edges ... of the vector space, and the ... A formula to compute the volume of an ...

  6. Platonic solid - Wikipedia

    en.wikipedia.org/wiki/Platonic_solid

    The tetrahedron is self-dual (i.e. its dual is another tetrahedron). The cube and the octahedron form a dual pair. The dodecahedron and the icosahedron form a dual pair. If a polyhedron has Schläfli symbol {p, q}, then its dual has the symbol {q, p}. Indeed, every combinatorial property of one Platonic solid can be interpreted as another ...

  7. Cayley–Menger determinant - Wikipedia

    en.wikipedia.org/wiki/Cayley–Menger_determinant

    In linear algebra, geometry, and trigonometry, the Cayley–Menger determinant is a formula for the content, i.e. the higher-dimensional volume, of a -dimensional simplex in terms of the squares of all of the distances between pairs of its vertices.

  8. Murakami–Yano formula - Wikipedia

    en.wikipedia.org/wiki/Murakami–Yano_formula

    In geometry, the Murakami–Yano formula, introduced by Murakami & Yano (2005), is a formula for the volume of a hyperbolic or spherical tetrahedron given in terms of its dihedral angles. References [ edit ]

  9. Cauchy stress tensor - Wikipedia

    en.wikipedia.org/wiki/Cauchy_stress_tensor

    The stress vector on this plane is denoted by T (n). The stress vectors acting on the faces of the tetrahedron are denoted as T (e 1), T (e 2), and T (e 3), and are by definition the components σ ij of the stress tensor σ. This tetrahedron is sometimes called the Cauchy tetrahedron.