Question

When an octahedron is truncated from every corner at a distance $\frac{a}{4}$ (a = side length of octahedral). What is the difference in the number of hexagonal faces and square faces created after truncation?

Answer 1

Every triangular face of octahedron is converted to an hexagonal face and every corner is converted to a square planar face after truncation.
Since, octahedron contains 8 triangular faces and 6 corners, so difference in number of hexagonal to square faces = 8 - 6 = 2