Mono-Pentahex Puzzles.
These puzzles use a full set of 22 pentahexes, seven tetrahexes, three trihexes, dihex and monohex. Together these pieces cover an area of 150 unit hexagons.
Snowflakes and Propellers
| Propeller puzzles have six identical blades, with the remaining pieces used to make a body with six-fold symmetry. Snowflakes are propellers with reflective symmetry for both body and blades. | ||||||||||||
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Blade Size (6 copies) |
8 | 9 | 10 | 13 | 14 | 15 | 18 | 19 | 20 | 23 | 24 | 25 |
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Body Size |
102 | 96 | 90 | 72 | 66 | 60 | 42 | 36 | 30 | 12 | 6 | 0* |
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| * propellers with 25-cell blades include shapes formed from the symmetric sextuplets. Only sextuplets with horizontal reflective symmetry can form snowflakes, but other solutions are possible with asymmetric blades. | ||||||||||||
Narcissi
| Create any shape with full six-fold symmetry. Patterns include all symmetric arrangements of snowflake solutions from the last puzzle, but many more are also possible. Patterns may contain a single hole at the centre, or multiple holes. The area of these holes will be 1 + multiple of six, and the holes may all be unit "portholes", or a mixture of sizes. | |||||||||||
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Enclosed Area |
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| Holes |
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7 | 13 | 19 | 25 | 31 | 37 | 43 | 49 | 55 | 61 |
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| 7 | X |
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| 13 | X | X |
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| 19 | X | X | X |
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| 25 | X | X | X | X |
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| 31 | X | X | X | X | X |
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| 37 | X | X | X | X | X | X |
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| 43 | X | X | X | X | X | X | X |
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| 67 | 73 | 79 | 85 | 91 | 97 | 103 | 109 | 115 | 121 | 127 | |
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| 13 |
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| 19 |
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| 25 |
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| 31 |
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| 37 |
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| 133 | 139 | 145 | 151 | 157 | 163 | 169 | 175 | 181 | 187 | 193 | |
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| 13 |
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| 19 |
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| 25 |
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| 31 |
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| 199 | 205 | 211 | 217 | 223 | 229 | 235 | 241 | 247 | 253 | 259 | |
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| 13 |
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| 19 |
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| 25 |
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| 265 | 271 | 277 | 283 | 289 | 295 | 301 | 307 | 313 | 319 | 325 | |
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| 13 |
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| 19 |
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| 331 | 337 | 343 | 349 | 355 | 361 | 367 | 373 | 379 | 385 | 391 | |
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| 397 | 403 | 409 | 415 | 421 | 427 | 433 | 439 | 445 | 451 | ||
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Portholes
| Create a pattern which encloses the maximum number of unit holes. Here are my best results for the different types of symmetry. | ||||||||||
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Type of Symmetry |
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| Full | Sextarotary | Ternary & Horizontal | Ternary & Vertical | Trirotary | Double Bilateral | Birotary | Horizontal | Vertical | None | |
| Holes |
43 |
43 | 46 | 46 | 46 | 48 | 48 | 48 | 48 | 49? |
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Replicas
| Create multiple copies of a pattern. Here are examples for the different types of symmetry. | |||||||||
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Type of Symmetry |
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| Copies | Full | Sextarotary | Ternary & Horizontal | Ternary & Vertical | Trirotary | Double Bilateral | Birotary | Horizontal | Vertical |
| 2 | X | X |
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| 3 | X | X | X | X | X |
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| 6 | ? | ? | ? |
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* the dihex piece is omitted when making patterns with four copies. |
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