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A scalenohedron is similar to a bipyramid; the difference is that the scalenohedra has a zig-zag pattern in the middle edges. [ 17 ] It has two apices and 2 n basal vertices, 4 n faces, and 6 n edges; it is topologically identical to a 2 n -gonal bipyramid, but its 2 n basal vertices alternate in two rings above and below the center.
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Regular polyhedron. Platonic solid: . Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot ...
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
A polyhedron (or polytope in general) is k-isohedral if it contains k faces within its symmetry fundamental domains. [5] Similarly, a k-isohedral tiling has k separate symmetry orbits (it may contain m different face shapes, for m = k, or only for some m < k).
In the hexagonal family, the crystal is conventionally described by a right rhombic prism unit cell with two equal axes (a by a), an included angle of 120° (γ) and a height (c, which can be different from a) perpendicular to the two base axes.
An example of the tetragonal crystals, wulfenite Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system.
The prismatic crystals are often terminated by the scalenohedron and the obtuse rhombohedron, thus resembling calcite (dog-tooth-spar) in habit. The color is scarlet-vermilion and the luster adamantine; crystals are transparent and very brilliant, but on exposure to light they soon become dull black and opaque.