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Volume of octahedron.

Source: AMC 10 2006A, Problem 24

February 6, 2006
geometry3D geometryoctahedrontetrahedronpyramidAMC

Problem Statement

Centers of adjacent faces of a unit cube are joined to form a regular octahedron. What is the volume of this octahedron? <spanclass=′latex−bold′>(A)</span>18<spanclass=′latex−bold′>(B)</span>16<spanclass=′latex−bold′>(C)</span>14<spanclass=′latex−bold′>(D)</span>13<spanclass=′latex−bold′>(E)</span>12 <span class='latex-bold'>(A) </span> \frac 18 \qquad <span class='latex-bold'>(B) </span> \frac 16 \qquad <span class='latex-bold'>(C) </span> \frac 14 \qquad <span class='latex-bold'>(D) </span> \frac 13 \qquad <span class='latex-bold'>(E) </span> \frac 12
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