A *compatibility figure* for two or more polyforms
is a figure that can be tiled with any of them.
In 2004, Livio Zucca published Pentomino
Odd Pairs, showing minimal known compatibility figures
for every pair of pentominoes, using an odd number of each.

Here I show minimal known compatibility figures for
every pair of pentacubes, using an odd number 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 solve an unsolved case, or find a smaller solution than one
given here, please write.

See also Pentacube Compatibility.

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 | 3 | 3 | 9 | 3 | 3 | 21 | 3 | 3 | 3 | 7 | 5 | 5 | 3 | 5 | 3 | 9 | 5 | 9 | 9 | 7 | 3 | 7 | |||||||

B | 3 | 3 | 3 | 3 | 5 | 3 | 5 | 3 | 3 | 3 | 3 | 3 | 3 | 5 | 3 | 5 | 3 | 5 | 5 | 3 | 5 | ||||||||

E | 3 | 3 | 3 | 3 | 3 | 3 | 15 | 3 | 3 | 3 | 5 | 5 | 3 | 3 | 3 | 3 | 3 | 5 | 5 | 5 | 5 | 3 | 5 | 9 | 3 | 5 | |||

F | 3 | 3 | 5 | 3 | 5 | 3 | 5 | 3 | 3 | 3 | 3 | 5 | 5 | 5 | 5 | 5 | 7 | 3 | 5 | ||||||||||

G | 3 | 3 | 5 | 15 | 3 | 3 | 3 | 3 | 5 | 3 | 5 | 3 | 3 | 3 | 3 | 5 | 7 | 9 | 3 | 7 | 25 | 5 | 5 | ||||||

H | 3 | 9 | 3 | 3 | 3 | 3 | 7 | 3 | 3 | 3 | 3 | 3 | 5 | 3 | 5 | 3 | 5 | 3 | 9 | 3 | 5 | ||||||||

I | 3 | 15 | 3 | – | 5 | 5 | 7 | 13 | 11 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | |||||||||||||

J | 3 | 3 | 3 | 5 | 3 | 3 | 3 | 3 | 3 | 5 | 5 | 3 | 3 | 3 | 5 | 9 | 3 | 3 | |||||||||||

K | 5 | 7 | 9 | 3 | 3 | 3 | 3 | 3 | 3 | 7 | 5 | 15 | 3 | 3 | |||||||||||||||

L | 9 | 3 | 3 | 3 | 5 | 3 | 3 | 3 | 3 | 5 | 23 | 3 | 3 | ||||||||||||||||

M | 7 | 3 | 3 | 3 | 9 | 7 | 9 | 9 | 7 | 3 | 5 | 7 | |||||||||||||||||

N | 3 | 3 | 3 | 3 | 5 | 5 | 3 | 3 | 15 | 3 | 7 | ||||||||||||||||||

P | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 7 | 3 | 3 | |||||||||||||||||||

Q | 3 | 3 | 7 | 3 | 3 | 3 | 17 | 3 | 5 | ||||||||||||||||||||

R | 3 | 3 | 3 | 5 | 5 | 7 | 3 | 9 | 3 | 3 | |||||||||||||||||||

S | 3 | 3 | 3 | 7 | 5 | – | 3 | 3 | |||||||||||||||||||||

T | 3 | 7 | 9 | 17 | 3 | 9 | |||||||||||||||||||||||

U | 7 | 9 | – | 5 | 11 | ||||||||||||||||||||||||

V | 9 | – | 5 | 7 | |||||||||||||||||||||||||

W | 19 | 5 | 5 | ||||||||||||||||||||||||||

X | 5 | 15 | |||||||||||||||||||||||||||

Y | 5 | ||||||||||||||||||||||||||||

Z |

Last revised 2022-02-24.

Back to Pairwise Compatibility < Polyform Compatibility < Polyform Curiosities

Col. George Sicherman [ HOME | MAIL ]