Sierpinski Volumes

Sierpinski sieves, are fractals with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. It is a mathematically generated pattern that is reproducible at any magnification or reduction.
This page shows some more Sierpinski shapes made using 3-dimensional platonic solids as the base. It uses the random jump technique for creating the shapes.

Sphere

jsfiddle

Sphere(BufferGeometry)

jsfiddle

Cube

jsfiddle

Cube(BufferGeometry)

jsfiddle

Pyramid

jsfiddle

Pyramid(BufferGeometry)

jsfiddle

Icosahedron

jsfiddle

Icosahedron(BufferGeometry)

jsfiddle

Octahedron

jsfiddle

Octahedron(BufferGeometry)

jsfiddle

Dodecahedron

jsfiddle

Dodecahedron(BufferGeometry)

jsfiddle