Catalogue of Besźel Polycubes
Introduction
A polycube is a solid made of equal cubes joined
face to face.
A Besźel Polycube is
a polycube, each of whose cells has
at least two even coordinates.
An Ul Qoma Polycube is
a polycube, each of whose cells has
at least two odd coordinates.
Besźel as a whole looks like this diagram, extended to infinity
in all directions:
Ul Qoma looks the same, only shifted and in a different color.
Besźel and Ul Qoma are independent and mutually hostile
city-states interspersed on common territory in China Miéville's
novel The City &
the
City.
Enumeration
Two-sided polycubes are identified with their mirror images.
One-sided polycubes are distinguished from their mirror images.
| Cells
| Two-Sided
A292157
| One-Sided
A292065 |
|---|
| 1 | 1 | 1 |
| 2 | 1 | 1 |
| 3 | 2 | 2 |
| 4 | 4 | 4 |
| 5 | 11 | 12 |
| 6 | 23 | 27 |
| 7 | 80 | 106 |
| 8 | 230 | 339 |
| 9 | 837 | 1336 |
| 10 | 2935 | 5029 |
The diagrams below show two-sided Besźel Polycubes.
Monocube
Dicube
Tricubes
Tetracubes
Pentacubes
Hexacubes
Heptacubes
Last revised 2018-03-10.
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Col. George Sicherman
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