AMC 10A 2006 Problem 24

Past Contests AMC 10 AMC 10A - 2006
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Centers of adjacent faces of a unit cube are joined to form a regular octahedron. What is the volume of this octahedron?

Answer Choices
A. \dfrac{1}{8}
B. \dfrac{1}{6}
C. \dfrac{1}{4}
D. \dfrac{1}{3}
E. \dfrac{1}{2}