Call a polyhex convex if the region enclosed by joining centers of adjacent cells is convex. A badge is a convex polyhex with 3-rotary symmetry and horizontal mirror symmetry. Here I tile minimal known badges with copies of two pentahexes so that copies of the second pentahex do not touch.
See also
| Isolated Pentahex | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | C | D | E | F | H | I | J | K | L | N | P | Q | R | S | T | U | V | W | X | Y | Z | |
| A | 234 | 9 | 2 | 165 | 66 | 9 | 30 | 126 | 24 | 15 | 32 | 18 | 18 | 276 | 213 | 84 | 33 | ? | 18 | 12 | 9 | |
| C | ? | 5 | ? | ? | ? | ? | ? | 18 | ? | ? | 84 | ? | ? | ? | ? | ? | ? | 12 | ? | ? | ? | |
| D | 12 | 5 | 5 | 9 | 12 | 9 | 12 | 9 | 9 | 5 | 5 | 9 | 5 | 11 | 12 | × | 9 | 12 | 9 | 2 | 12 | |
| E | 2 | 93 | 24 | 12 | 63 | 11 | 21 | 29 | 27 | 38 | 9 | 18 | 9 | 87 | 288 | 42 | 93 | 51 | 11 | 33 | 21 | |
| F | 15 | ? | 15 | 12 | 12 | 15 | ? | 51 | 15 | 27 | 33 | 15 | 27 | ? | ? | ? | ? | 126 | 15 | 54 | 54 | |
| H | ? | 12 | ? | 33 | 33 | 60 | 54 | ? | 54 | 33 | 15 | ? | 33 | ? | ? | 15 | ? | ? | ? | 15 | ? | |
| I | 18 | 123 | 12 | 18 | 126 | 84 | 18 | 84 | 15 | 27 | 15 | 66 | 51 | 126 | ? | ? | 18 | ? | ? | 12 | 51 | |
| J | 54 | ? | 15 | 72 | ? | ? | 15 | 12 | 75 | 12 | 12 | 75 | 18 | ? | 84 | ? | 15 | ? | 18 | 9 | 75 | |
| K | 9 | 54 | 9 | 29 | 33 | ? | 24 | 15 | 12 | 33 | 15 | ? | 33 | ? | ? | ? | 12 | ? | ? | 9 | ? | |
| L | 12 | 12 | 5 | 12 | 12 | 12 | 9 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 18 | 12 | 11 | 12 | |
| N | 9 | 15 | 9 | 9 | 15 | 12 | 9 | 9 | 12 | 9 | 15 | 12 | 12 | 15 | 15 | 18 | 15 | 18 | 15 | 9 | 15 | |
| P | 9 | 12 | 5 | 5 | 5 | 12 | 9 | 12 | 12 | 12 | 9 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 9 | 12 | |
| Q | 9 | 15 | 21 | 18 | 54 | ? | 33 | 12 | ? | 15 | 18 | 12 | 66 | ? | ? | 15 | 33 | ? | ? | 9 | ? | |
| R | 54 | 33 | 9 | ? | 54 | ? | 33 | 18 | 141 | 32 | 12 | 15 | ? | ? | ? | 15 | 12 | ? | ? | 12 | 72 | |
| S | ? | ? | 15 | ? | ? | ? | ? | ? | ? | ? | ? | 63 | ? | ? | ? | ? | 12 | ? | ? | 9 | ? | |
| T | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | |
| U | ? | ? | ? | ? | ? | ? | ? | ? | 168 | ? | ? | ? | ? | ? | ? | ? | 15 | ? | ? | 9 | ? | |
| V | 51 | 18 | 15 | 29 | 171 | 129 | 15 | 36 | 51 | 18 | 27 | 12 | 29 | 33 | 15 | 29 | 123 | 165 | 60 | 12 | 29 | |
| W | ? | 12 | ? | 9 | ? | ? | ? | ? | ? | 12 | ? | 12 | ? | 51 | ? | ? | ? | ? | ? | 165 | ? | |
| X | 9 | ? | ? | 51 | 63 | ? | ? | ? | ? | ? | ? | 147 | ? | ? | ? | ? | ? | ? | ? | ? | ? | |
| Y | 9 | 11 | 2 | 15 | 9 | 15 | 9 | 3 | 9 | 9 | 9 | 9 | 12 | 9 | 9 | 15 | 12 | 9 | 12 | 11 | 12 | |
| Z | 12 | 18 | 15 | 9 | 60 | ? | 9 | 15 | ? | 12 | 15 | 12 | ? | 15 | ? | ? | 33 | 15 | ? | ? | 9 | |
Last revised 2025-06-18.