Question

Which of the following will not form a polyhedron?

• A. $3$ triangles
• B. $2$ triangles and $3$ parallelogram
• C. $8$ triangles
• D. $1$ pentagon and $5$ triangles

Answer 1

The correct option is A

$3$ triangles

Step 1. Explanation for the correct option.

A polyhedron is a three-dimensional variant of the most common polytope, which defines an arbitrary dimension.

For option (A): $3$ triangles

A polyhedron must have more than four faces, three triangles will not create a polyhedron. So, it is not possible in $3$ triangles which have $3$ faces only.

Hence, the correct option is “Option A”.

Step 2. Explanation for incorrect options.

For option (B): $2$ triangles and $3$ parallelogram

A polyhedron is described as two triangles and three parallelograms. Sides connect at edges, which are called line segments, and the edges meet at vertices, which are called points.

For option (C): $8$ triangles

Since the polyhedron has $8$ faced, it could be formed by $8$ triangles.

For option (D): $1$ pentagon and $5$ triangles

A polyhedron formed by a pentagon and five triangles meets the definition. Faces meet at edges, which are called line segments, and the edges meet at vertices, which are called points.

Hence, the correct option is “Option A”.