Question

When an octahedron is truncated from each corner then which of the following options is not true about it?

• A. Total faces in the truncated octahedron is 14
• B. Total edges in truncated octahedron is 36
• C. Total vertices in truncated octahedron is 24
• D. Ratio of hexagonal faces to square faces is 2:3

Answer 1

The correct option is D Ratio of hexagonal faces to square faces is 2:3

A octahedron contains:
i) 6 vertices, ii) 8 triangular faces, iii) 12 edges
When a octahedron is truncated at each corner following things happen:
i) 6 square faces are generated at the corners and all 8 triangular faces are converted to hexagonal faces leading to total of 14 faces.
ii) 36 total edges are present $6\times 4+12=36$.
iii) 24 vertices are present $6\times 4=24$.
So the ratio of hexagonal faces to square faces is 4:3.