Catalogue of Unitary Polycubes


A polycube is unitary if each of its faces is a single square, a monomino. A unitary polycube may contain holes, provided that the holes are unitary.

Here I show all unitary polycubes with at most 25 cells. I do not distinguish mirror images. Cross-sections are shown from the bottom up. Unitary polycubes that are known to be able to fill space are marked with an asterisk (*). That which is known to fill space only if it may be reflected is marked with a double dagger ().

If you find an omission, please write.

Bryce Herdt identified many space-filling unitary polycubes, and supplied a simple method of proving that a polycube fills space by translation.


Cells 171213161718192021222324 25
Polycubes 111113223416211924

1 Cell

7 Cells

12 Cells

13 Cells

16 Cells

17 Cells

18 Cells

19 Cells

20 Cells

21 Cells

22 Cells

23 Cells

24 Cells

25 Cells

Last revised 2023-03-19.

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Col. George Sicherman [ HOME | MAIL ]