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An octahedral hole reads at the center of six equidistant spheres whose centers define an octahedron. Three of these six spheres lie in one closest packed layer and three lie in the adjacent layer [Fig. 16.36(c)]. These six spheres can be rotated to show the octahedron more clearly (Fig. 16.37).<br>Since the edges of all six spheres are exactly the same distance from the center of the octahedral hole, we can calculate the radius of this hole easily by focusing on the four spheres whose centers form a square (Fig. 16.37). Note from Fig. 16.37 that R is the radius of the packed spheres, r is the radius of the octahedral hole, and d is the length of the diagonal of the square. From the Pythagorean theorem, ...
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