IKMC 2017 - Grades 11-12 - Self-study Question 24

Question 24

We look at a regular tetrahedron with volume 1. Its four vertices are cut off by planes that go through the midpoints of the respective edges (see diagram). How big is the volume of the remaining solid?

Question illustration

$\frac45$
$\frac34$
$\frac23$
$\frac12$
$\frac13$