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 $$a$$: $$$A=5\cdot \sqrt{3} \cdot a^2 \\ V=\dfrac{5}{12}(\sqrt{5}+3)a^3$$$