IKMC 2018 - Grades 11-12 - Self-study Question 14

Question 14

An octahedron is inscribed into a die with side length 1. The vertices of the octahedron are the midpoints of the faces of the die. How big is the volume of the octahedron?

Question illustration

$\frac13$
$\frac14$
$\frac15$
$\frac16$
$\frac18$