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  2. Cubical complex - Wikipedia

    en.wikipedia.org/wiki/Cubical_complex

    The dimension of the face is the number of indices such that = [,]; a face of dimension , or -face, is itself naturally a unit elementary cube of dimension , and is sometimes called a subcube of . One can also regard ∅ {\textstyle \emptyset } as a face of dimension − 1 {\textstyle -1} .

  3. Geometry - Wikipedia

    en.wikipedia.org/wiki/Geometry

    A surface is a two-dimensional object, such as a sphere or paraboloid. [55] In differential geometry [53] and topology, [49] surfaces are described by two-dimensional 'patches' (or neighborhoods) that are assembled by diffeomorphisms or homeomorphisms, respectively. In algebraic geometry, surfaces are described by polynomial equations. [54]

  4. Volume form - Wikipedia

    en.wikipedia.org/wiki/Volume_form

    In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold M {\displaystyle M} of dimension n {\displaystyle n} , a volume form is an n {\displaystyle n} -form.

  5. Volume - Wikipedia

    en.wikipedia.org/wiki/Volume

    In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary.

  6. Five-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Five-dimensional_space

    Therefore, the geometry of the 5th dimension studies the invariant properties of such space-time, as we move within it, expressed in formal equations. [11] Fifth dimensional geometry is generally represented using 5 coordinate values (x,y,z,w,v), where moving along the v axis involves moving between different hyper-volumes. [12]

  7. 5-simplex - Wikipedia

    en.wikipedia.org/wiki/5-simplex

    In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets.It has a dihedral angle of cos −1 (⁠ 1 / 5 ⁠), or approximately 78.46°.

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