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 six L-shaped polycubes that can be tiled with the set of 29 pentacubes. There are many 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.
This polycube can also be tiled with copies of any of 9 single pentacubes: E, E′, I, J, J′, L, N, P, and Y.
This polycube can also be tiled with copies of any of 11 single pentacubes: E, E′, H, H′, I, J, J′, L, N, P, and Y.
This polycube can also be tiled with copies of any of 10 single pentacubes: E, E′, I, J, J′, L, N, P, Q, and Y.
This polycube can also be tiled with copies of any of 4 single pentacubes: I, L, P, and Y.
This prism was first tiled by Torsten Sillke. Naturally it can also be tiled by copies of the P pentacube alone.
Last revised 2026-10-05.