Cutting off tetrahedral corners off a cube...

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Problem:

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Solution:

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The part I don't get is circled in red - why is the side length of the tetrahedron equal to square root 2? If the tetrahedra meet at the midpoints of the cube, then surely the side length of the tetrahedron is equal to 1?

Apologies if I am being obtuse - could someone clarify? Many thanks.