An arrangement in three-dimensional space of n congruent cubes joined to one another by at least one of their faces.

  • A polycube formed by joining 2 cubes is called a dicube.
  • Polycubes formed by joining 3 cubes are called tricubes. There are 2 tricubes.
  • Polycubes formed by joining 4 cubes are called tetracubes. There are 8 tetracubes.
  • Polycubes formed by joining 5 cubes are called pentacubes. There are 29 pentacubes.
  • Polycubes formed by joining 6 cubes are called hexacubes. There are 166 hexacubes.


This is a pentacube:

This photo shows a pyramidal arrangement of 166 hexacubes.
This structure was designed by A. Clarke and assembled by Pierre Mathieu.


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