Mono-Pentahex Puzzles

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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.

Blade Size (6 copies)

8 9 10 13 14 15 18 19 20 23 24 25

Body Size

102 96 90 72 66 60 42 36 30 12 6 0*
Snowflakes
Propellers
* 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.
 

Enclosed Area

Holes

1

7 13 19 25 31 37 43 49 55 61
1
7 X
13 X X
19 X X X
25 X X X X
31 X X X X X
37 X X X X X X
43 X X X X X X X    
                       
  67 73 79 85 91 97 103 109 115 121 127
1
7
13
19
25
31
37                  
                       
  133 139 145 151 157 163 169 175 181 187 193
1
7
13
19
25
31
                       
  199 205 211 217 223 229 235 241 247 253 259
1
7
13
19
25      
31                    
                       
  265 271 277 283 289 295 301 307 313 319 325
1
7
13
19  
                       
  331 337 343 349 355 361 367 373 379 385 391
1
                       
  397 403 409 415 421 427 433 439 445 451  
1  

 

Portholes

 

     Create a pattern which encloses the maximum number of unit holes. Here are my best results for the different types of symmetry.
 

Type of Symmetry

  Full Sextarotary Ternary & Horizontal Ternary & Vertical Trirotary Double Bilateral Birotary Horizontal Vertical None
Holes

43

43 46 46 46 48 48 48 48 49?
   

 

Replicas

 

     Create multiple copies of a pattern. Here are examples for the different types of symmetry.
 

Type of Symmetry

Copies Full Sextarotary Ternary & Horizontal Ternary & Vertical Trirotary Double Bilateral Birotary Horizontal Vertical
2 X X
3 X X X X X
4*
5 ? ?
6 ? ? ?

     * the dihex piece is omitted when making patterns with four copies.

 

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