L Shapes from the 29 Pentacubes


A polycube is a solid made of equal cubes joined face to face, and a pentacube is a polycube with 5 cells. There are 29 pentacubes, distinguishing mirror images:

The letters shown in black are my names. Mirror images of chiral pentacubes are indicated with ; e.g., G′ is the mirror image of G. The green symbols are Kate Jones's names. The red symbols are Donald Knuth's names.

I define an L-shaped polycube as a polycube prism whose base is L-shaped; that is, it consists of a rectangle from one corner of which a smaller rectangle has been excised. I do not require that the arms have the same width.

Here I show an L-shaped polycube that can be tiled with the set of 29 pentacubes. There may be others.

See also L Shapes from Pentacube Pairs.

This polycube can also be tiled with copies of any of 13 single pentacubes: B, E, E′, H, H′, I, J, J′, L, N, P, Q, and Y.

For E′, H′, and J′, vertically reflect the tilings for For E, H, and J.

Last revised 2022-11-14.

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Col. George Sicherman [ HOME | MAIL ]