Menger Sponge Slices
Start with a cube. Draw nine squares on each face of the cube, forming a 3×3 pattern. Drill out the middle squares across the cube. Take the eight squares left on each face and draw the 3×3 pattern for each one. Drill straight through again. Keep doing that; the Menger sponge fractal is the limit of the process.[more]
This Demonstration slices the Menger sponge by a plane perpendicular to a main diagonal at certain distances.[less]
Snapshot 1: a cube sliced diagonally reveals a hexagonal face
Snapshot 2: different depths of slices reveal similar shapes
Snapshot 3: with no slice, the figure is the Menger cube
Inspired by John D. Cook .
 J. D. Cook, "Code to Slice Open a Menger Sponge," John D. Cook (blog). (Mar 23, 2014) www.johndcook.com/blog/2011/08/30/slice-a-menger-sponge.
"Menger Sponge Slices"
Wolfram Demonstrations Project
Published: March 26 2015