A polyhex is said to be hex-convex if the shape formed by joining the centers of its adjacent cells is convex. Here I study the problem of arranging copies of two given pentahexes to form a hex-convex shape with any number of isolated monohex holes.
| A | C | D | E | F | H | I | J | K | L | N | P | Q | R | S | T | U | V | W | X | Y | Z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | • | 4 | 2 | 2 | 6 | 9 | 4 | 3 | 4 | 4 | 3 | 3 | 4 | 6 | 10 | 12 | 2 | 5 | 10 | 3 | 4 | 4 |
| C | 4 | • | 2 | 2 | 4 | 6 | 6 | 3 | 4 | 4 | 4 | 4 | 3 | 4 | 4 | 5 | 3 | 6 | 4 | 3 | 2 | 5 |
| D | 2 | 2 | • | 3 | 4 | 8 | 3 | 2 | 4 | 3 | 2 | 3 | 4 | 3 | 3 | 7 | 2 | 3 | 7 | 3 | 2 | 6 |
| E | 2 | 2 | 3 | • | 4 | 6 | 4 | 4 | 6 | 4 | 4 | 3 | 4 | 4 | 9 | 10 | 4 | 3 | 6 | 4 | 5 | 5 |
| F | 6 | 4 | 4 | 4 | • | 12 | 4 | 4 | 10 | 4 | 4 | 4 | 7 | 8 | 17 | 32 | 4 | 4 | 22 | 7 | 4 | 11 |
| H | 9 | 6 | 8 | 6 | 12 | • | 6 | 3 | — | 4 | 5 | 5 | 12 | 10 | — | — | 3 | 4 | — | — | 5 | — |
| I | 4 | 6 | 3 | 4 | 4 | 6 | • | 4 | 6 | 3 | 3 | 3 | 6 | 4 | 6 | 10 | 5 | 5 | 6 | 7 | 3 | 6 |
| J | 3 | 3 | 2 | 4 | 4 | 3 | 4 | • | 3 | 3 | 2 | 2 | 3 | 4 | 5 | 4 | 3 | 3 | 4 | 4 | 3 | 4 |
| K | 4 | 4 | 4 | 6 | 10 | — | 6 | 3 | • | 3 | 4 | 3 | 10 | 10 | — | — | 6 | 4 | — | — | 4 | — |
| L | 4 | 4 | 3 | 4 | 4 | 4 | 3 | 3 | 3 | • | 2 | 2 | 4 | 5 | 5 | 6 | 3 | 4 | 4 | 3 | 4 | 3 |
| N | 3 | 4 | 2 | 4 | 4 | 5 | 3 | 2 | 4 | 2 | • | 3 | 4 | 4 | 5 | 5 | 2 | 2 | 6 | 3 | 2 | 4 |
| P | 3 | 4 | 3 | 3 | 4 | 5 | 3 | 2 | 3 | 2 | 3 | • | 3 | 3 | 3 | 4 | 3 | 2 | 4 | 5 | 2 | 4 |
| Q | 4 | 3 | 4 | 4 | 7 | 12 | 6 | 3 | 10 | 4 | 4 | 3 | • | 6 | 10 | 11 | 2 | 4 | 10 | 10 | 4 | 10 |
| R | 6 | 4 | 3 | 4 | 8 | 10 | 4 | 4 | 10 | 5 | 4 | 3 | 6 | • | 9 | 10 | 3 | 6 | 9 | 7 | 3 | 10 |
| S | 10 | 4 | 3 | 9 | 17 | — | 6 | 5 | — | 5 | 5 | 3 | 10 | 9 | • | — | 10 | 3 | — | — | 3 | — |
| T | 12 | 5 | 7 | 10 | 32 | — | 10 | 4 | — | 6 | 5 | 4 | 11 | 10 | — | • | 10 | 10 | — | — | 5 | — |
| U | 2 | 3 | 2 | 4 | 4 | 3 | 5 | 3 | 6 | 3 | 2 | 3 | 2 | 3 | 10 | 10 | • | 4 | 10 | 5 | 3 | 6 |
| V | 5 | 6 | 3 | 3 | 4 | 4 | 5 | 3 | 4 | 4 | 2 | 2 | 4 | 6 | 3 | 10 | 4 | • | 4 | 5 | 4 | 4 |
| W | 10 | 4 | 7 | 6 | 22 | — | 6 | 4 | — | 4 | 6 | 4 | 10 | 9 | — | — | 10 | 4 | • | — | 5 | — |
| X | 3 | 3 | 3 | 4 | 7 | — | 7 | 4 | — | 3 | 3 | 5 | 10 | 7 | — | — | 5 | 5 | — | • | 5 | — |
| Y | 4 | 2 | 2 | 5 | 4 | 5 | 3 | 3 | 4 | 4 | 2 | 2 | 4 | 3 | 3 | 5 | 3 | 4 | 5 | 5 | • | 4 |
| Z | 4 | 5 | 6 | 5 | 11 | — | 6 | 4 | — | 3 | 4 | 4 | 10 | 10 | — | — | 6 | 4 | — | — | 4 | • |
Last revised 2026-03-29.