Sierpinski's triangle is formed by recursively deleting medial triangles from an original triangle. (The vertices of the medial triangle of a triangle T are the midpoints of the sides of T.) This Demonstration maps Sierpinski triangles onto the faces of polyhedra with all triangular faces.
jgkogan/Mapping-Sierpinski-Triangles-onto-Polyhedra
Sierpinski's triangle is formed by recursively deleting medial triangles from an original triangle. (The vertices of the medial triangle of a triangle T are the midpoints of the sides of T.) This Demonstration maps Sierpinski triangles onto the faces of polyhedra with all triangular faces.
Mathematica