Pentatwig Puzzles
These puzzles use the 12 pentatwigs. The pieces cover 60 unit line segments.
Geometric Forms
Use all pieces to make a symmetric pattern. Here are examples for the different types of symmetry. George Sicherman confirmed that there are no full or 6-rotary solutions, with an exhaustive search of all 2275 patterns. Type of Symmetry
Ternary & Horizontal Ternary & Vertical Trirotary Double Bilateral Horizontal Vertical Birotary Here is a page of these puzzles which you can print and solve: Polytwig Symmetry Puzzles
Pairs & Triplets
Use all the pieces to make two or three identical copies of a pattern.
Polyforms are compatible if there is a shape that can be tiled by each. You can find more about Polyform Compatibility at George Sicherman's Polyform Curiosities website. Here are minimal known compatibilities for the pentatwigs. George improved some of my solutions, marked *.
- 4* 3 6 3 4 ? ? 4 ? 3 ? 4* - R 2 4* 2 3 2 2 2 R R 3 R - 4* 3 R 2 2 2 R 3 2 6 2 4* - ? 6 3 2 2 3 6 6 3 4* 3 ? - 6 3 3 3 ? 4 ? 4 2 R 6 6 - 3 6 6 2 6 ? ? 3 2 3 3 3 - 3 3 3 2* 6 ? 2 2 2 3 6 3 - 2 R R R 4 2 2 2 3 6 3 2 - 6 3 2 ? 2 R 3 ? 2 3 R 6 - 6 R 3 R 3 6 4 6 2* R 3 6 - 6 ? R 2 6 ? ? 6 R 2 R 6 - 2 Tiles
3 Tiles
4 Tiles
6 Tiles
Reëntrant Solutions
Minimal known compatibilities for the tritwigs and tetratwigs, all found by George
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 the minimal solutions for the tri-, tetra- and pentatwigs. Tritwigs
Tetratwigs
Pentatwigs
A Galvagni Figure is one which can be tiled by a specific polyform in more than one way. You can find more about Galvagni Figures at George Sicherman's Polyform Curiosities website. Here are the minimal solutions for the pentatwigs, as found by George. Pentatwigs
