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Polygons - NEHSTechShowcase
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... As with triangles, there are several ways to classify quadrilaterals, depending on angles and side lengths. Classifying Quadrilaterals The following are several types of quadrilaterals. trapezoid - at least one pair of parallel sides parallelogram - both pairs of opposite sides are parallel kite - t ...
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... In the case of regular polygons, the formula for the number of triangles in a polygon is: Where…n is the number of sides (or vertices) Why? The triangles are created by drawing the diagonals from one vertex to all the others. Since there would be no diagonal drawn back to itself, and the diagonals t ...
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Regular polytope



In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube). The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians.Classically, a regular polytope in n dimensions may be defined as having regular facets [(n − 1)-faces] and regular vertex figures. These two conditions are sufficient to ensure that all faces are alike and all vertices are alike. Note, however, that this definition does not work for abstract polytopes.A regular polytope can be represented by a Schläfli symbol of the form {a, b, c, ...., y, z}, with regular facets as {a, b, c, ..., y}, and regular vertex figures as {b, c, ..., y, z}.
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