Tiling an N×N×N Cube with an N-Cube

A polycube is a solid made by joining 1 or more equal cubes face to face. An n-cube is a polycube with n cells.

An n-cube may be able to tile a cube with dimensions n×n×n. Here I show polycubes with 1–7 cells that are known to be able to do this.

I do not permit a polycube to be reflected. I show only one polycube of a pair of distinct mirror images.

In the diagrams, the cross-sections are shown from top to bottom.

If you find another polycube with n cells that can tile a cube with dimensions n×n×n, please write.

  • Monocube
  • Dicube
  • Tricubes
  • Tetracubes
  • Pentacubes
  • Hexacubes
  • Heptacubes
  • Octacubes

    • Monocube

    Dicube

    Tricubes

    Tetracubes

    Three of these tetracubes can each tile a 2×2×2 cube.

    Pentacubes

    Hexacubes

    Heptacubes

    Octacubes

    There are 280 octacubes that are known to be able to tile an 8×8×8 cube. That is too many tilings to show here. The picture below shows only the 280 octacubes. Only one of each mirror pair of octacubes is shown.

    Last revised 2026-06-27.

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    Col. George Sicherman [ HOME | MAIL ]