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Since the octahedral point group is common to the regular octahedron and the cube, we will refer indistinctly to it as octahedral or cubic throughout this paper. Similarly, we will generally use the term icosahedral polyhedron to refer to any polyhedron with icosahedral symmetry
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Since the octahedral point group is common to the regular octahedron and the cube, we will refer indistinctly to it as octahedral or cubic throughout this paper. Similarly, we will generally use the term icosahedral polyhedron to refer to any polyhedron with icosahedral symmetry
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While an Archimedean polyhedron has all its vertices equivalent and all its edges have the same length, in a generalized Archimedean polyhedron different sets of edges may have different lengths, resulting in some non-regular faces but fully retaining the symmetry of the ideal Archimedean polyhedron with regular polygonal faces
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While an Archimedean polyhedron has all its vertices equivalent and all its edges have the same length, in a generalized Archimedean polyhedron different sets of edges may have different lengths, resulting in some non-regular faces but fully retaining the symmetry of the ideal Archimedean polyhedron with regular polygonal faces
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Continuous shape and symmetry measures provide a quantitative indication of the distance of a molecular structure from having an ideal shape or a given symmetry, respectively. A zero value of a shape measure indicates that the structure under scrutiny has exactly the shape of the reference polyhedron. As a rule of thumb, values smaller than 0.1 correspond to minute deviations from the ideal shape, while a value of one unit or larger indicates an important distortion:
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