Icosahedron

An Icosahedron is the platonic solid with the most number of faces. It is well known for being the shape of some bacteria. It is what most people picture when they here complex dice.

Hypervolumes

 * vertex count = $$12$$
 * edge length = $$30l$$
 * surface area = $$5\sqrt { 3 } { l }^{ 2 }$$
 * surcell volume = $$\frac { 5(3+\sqrt { 5 } ) }{ 12 } { l }^{ 3 }$$

Subfacets

 * 12 points (0D)
 * 30 line segments (1D)
 * 20 triangles (2D)