Polygem Puzzles

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Mono- and Digem Puzzles

These puzzles use the monogem and the four digems. The pieces cover an area of 9 gems or 3 unit hexagons.

 

Geometric Forms

       Use all the pieces to make a symmetric pattern. Here are examples for the different types of symmetry. Click the images below to see a set of puzzles with solutions.

Type of Symmetry

Trirotary (1 Pattern) Birotary (8 Patterns) Horizontal (68 Patterns) Vertical (37 Patterns)

Trigem Puzzles

These puzzles use a full set of fifteen trigems. The pieces cover an area of 45 gems or 15 unit hexagons.

Geometric Forms

 

     Use all the pieces to make a symmetric pattern. Click the images below to see a set of puzzles with solutions.

Type of Symmetry

Full Sextarotary Ternary & Horizontal Ternary & Vertical Trirotary Double Bilateral Birotary Horizontal Vertical

 

Triplets

 

     Use all the pieces to make three identical copies of a pattern. Click the image below to see a set of puzzles with solutions.

Oddities & Compatibilities

      An oddity is a figure with binary symmetry formed by an odd number of copies of a polyform. Polyforms are compatible if there is a shape that can be tiled by each. You can find more about Polygem Oddities and Trigem Compatibility at George Sicherman's Polyform Curiosities website.

Baiocchi Figures

      A Baiocchi Figure is one with maximal symmetry for the set of polyforms. You can find more about Baiocchi Figures at George Sicherman's Polyform Curiosities website. Here are solutions for the di- and trigems. Other symmetrical constructions can be seen on my Polygem Symmetry Spectra page.

Mono-Trigem Puzzles

These puzzles use a full set of fifteen trigems, four digems and monogem. The pieces cover an area of 54 gems or 18 unit hexagons.

Geometric Forms

 

     Use all the pieces to make a symmetric pattern. Here are examples for the different types of symmetry. Click the images below to see a set of puzzles with solutions.

Type of Symmetry

Full Sextarotary Ternary & Horizontal Ternary & Vertical Trirotary Double Bilateral Birotary Horizontal Vertical

 

Pairs & Triplets

 

Use all the pieces to make two or three identical copies of a pattern. Click the images below to see a set of puzzles with solutions.

Triple Propellers

       Make a body with ternary symmetry, using one or more pieces. Use the remaining pieces to construct three identical blades.
Body  3 units 6 units 9 units 12 units 15 units 18 units
 
Blades
Body 21 units 24 units 27 units 30 units 33 units 36 units
 
Blades
Here is a page of these puzzles which you can print and solve: Mono- Trigem Propellers

 

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