UPSC 2014 CDS II Math Paper

There are 6 faces in a cube. Let each edge of the cube be a unit.
Length of each diagonal joining the opposite vertices of a face of the cube =√2a
Remember: Triangle formed by joining the end–points of the diagonals of any three coterminous faces forms an equilateral triangle.
One such equilateral triangle is shown in the given figure.
Now, joining any three vertices of a cube can form 8 such equilateral triangles.