A *diamond polyomino* is a polyomino in the form of an oblique
square
with four zigzag edges.

A *diamond prism polycube*
is a polycube prism whose base is a diamond polyomino.

Here I show the smallest known diamond prism polycubes
that can be tiled with
copies of of two different pentacubes, using at least one of each.
A prime mark (**′**) after a letter denotes a mirror image.
For example, **S′** is the mirror image of
**S**.
To see a tiling, click on the corresponding entry in the table below.
Missing entries indicate unsolved cases.

If you find a smaller solution, or solve an unsolved case, please write.

See also Tiling Triangular Prism Polycubes with Two Pentacubes and Tiling Pyramid Prism Polycubes with Two Pentacubes.

A | B | E | E′ | F | G | G′ | H | H′ | I | J | J′ | K | L | M | N | P | Q | R | R′ | S | S′ | T | U | V | W | X | Y | Z | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A | 4 | 4 | 10 | 10 | 10 | 7 | 4 | 10 | 4 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 4 | 10 | 10 | 3 | 4 | 10 | |||||||

B | 3 | 10 | 3 | 10 | 7 | 6 | 15 | 6 | 13 | 10 | 10 | 10 | 10 | 13 | 5 | 4 | 4 | 10 | 3 | 6 | 5 | ||||||||

E | 4 | 10 | 3 | 10 | 10 | 10 | 7 | 4 | 4 | 20 | 6 | – | 10 | 10 | 10 | 10 | 10 | 25 | 15 | 3 | 4 | 15 | 10 | 3 | 6 | 4 | |||

F | 20 | 34 | 13 | 15 | 34 | 20 | 106 | 17 | 17 | 34 | 34 | 34 | 17 | 10 | 20 | 17 | 5 | 20 | 29 | ||||||||||

G | – | 25 | 34 | 26 | 15 | 3 | 20 | 20 | – | 20 | 20 | 20 | – | – | – | 30 | 30 | 10 | 3 | 20 | 10 | 20 | 34 | ||||||

H | 34 | 13 | 15 | 15 | 34 | 20 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 34 | 30 | 10 | 15 | 34 | 10 | 20 | 34 | ||||||||

I | 13 | 6 | 5 | 25 | 13 | 5 | 13 | 25 | 25 | 6 | 7 | 13 | 13 | 6 | 13 | 13 | |||||||||||||

J | 15 | 15 | 15 | 20 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 3 | 15 | 15 | 15 | 20 | 4 | 15 | |||||||||||

K | 20 | – | – | – | 34 | 34 | – | 51 | 30 | – | 34 | 68 | 20 | – | |||||||||||||||

L | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 4 | 20 | 17 | 20 | 4 | 20 | ||||||||||||||||

M | – | – | 34 | – | – | – | 15 | – | 34 | – | 13 | – | |||||||||||||||||

N | – | 34 | 34 | 34 | 30 | 30 | 20 | 17 | 41 | 20 | – | ||||||||||||||||||

P | 34 | 34 | 34 | 20 | 15 | 15 | 17 | 15 | 17 | 20 | |||||||||||||||||||

Q | 34 | 34 | 20 | 10 | 20 | 34 | 10 | 20 | 34 | ||||||||||||||||||||

R | – | 34 | – | 51 | 10 | 30 | 34 | 10 | 20 | 34 | |||||||||||||||||||

S | – | 51 | 30 | 20 | 34 | – | 20 | – | |||||||||||||||||||||

T | 20 | 51 | 51 | – | 75 | – | |||||||||||||||||||||||

U | 4 | 10 | 3 | 4 | 51 | ||||||||||||||||||||||||

V | 20 | 30 | 4 | 51 | |||||||||||||||||||||||||

W | 5 | 13 | 17 | ||||||||||||||||||||||||||

X | 68 | – | |||||||||||||||||||||||||||

Y | 20 | ||||||||||||||||||||||||||||

Z |

Last revised 2024-02-08.

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Col. George Sicherman [ HOME | MAIL ]