Geometry
# Polyhedra

Given a regular tetrahedron with volume $1 \text{cm}^3$ and a cube with volume $1 \text{cm}^3$, which object has smaller surface area?

**Details and Assumptions**:

In a regular tetrahedron, all four faces are equilateral triangles, and

In a cube, all six faces are squares.

The dodecahedron has 12 pentagonal faces. Therefore it has $\frac{12 \times 5}{2} = 30$ edges.

The icosahedron has 20 equilateral triangular faces. Therefore it has $\frac{20 \times 3}{2} = 30$ edges.

**How many edges does a truncated icosahedron have?**