Icosahedron: Surface area and volume

The icosahedron is a regular polyhedron of $20$ faces. If the mentioned faces are equilateral triangles we will call it a regular icosahedron.

The following expressions allow us to find the area and volume of the icosahedron of edge $a$: $$A=5\cdot \sqrt{3} \cdot a^2 \\ V=\dfrac{5}{12}(\sqrt{5}+3)a^3$$