Scalenohedron

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A di--gonal scalenohedron is bounded by mutually congruent scalene triangles. As a convex polyhedron with and , it occurs as a crystal form of certain minerals.

Contributed by: Sándor Kabai, Gábor Gévay and Lajos Szilassi (July 2008)
Open content licensed under CC BY-NC-SA


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Consider a regular polygon with sides in a horizontal plane. Raise and lower its alternate vertices to get a regular skew polygon. Take its (vertical) axis of rotation, and, for some , choose a pair of points on this axis at heights and . Take each of those points as an apex connected to the vertices of the regular skew polygon by edges. These edges, together with the sides of the skew polygon, form the triangular faces of a general di--gonal scalenohedron. A general di--gonal scalenohedron is not necessarily a convex polyhedron. By moving the contols, you can see that in special cases bipyramids, streptohedra, rhombohedra, tetrahedra, and even the cube appear. In nature, the ditrigonal scalenohedron occurs as a well-known crystal form of calcspar (calcite). For , the name tetragonal scalenohedron is preferred for "di-digonal scalenohedron" (a crystal form of chalcopyrite, the most frequent ore of copper).



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