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. | ||||||||
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| Full | Sextarotary | Ternary & Horizontal | Ternary & Vertical | Trirotary | Double Bilateral | Birotary | Horizontal | Vertical |
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Pairs & Triplets
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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. |
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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 |
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| Body | 21 units | 24 units | 27 units | 30 units | 33 units | 36 units |
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| Here is a page of these puzzles which you can print and solve: Mono- Trigem Propellers | ||||||