Wei-Hwa Huang and Brendan Owens solved my various problems with tetracairos.
Related -- After being contacted by students of math teacher Odette De
Meulemeester from Belgium, Livio Zucca has made a new page about covering
areas with polyforms, you can see
it here. These are known as Farm problems, where the polyform
is used to make a fence. If you try to make two identical shapes
with a large hole, to problem becomes even harder. Also, trying to
make a symmetrical shape with the largest possible hole is quite hard.
Some Solvers: Brendan Owen and Wei-Hwa Huang
solved my Tetracairo problems. Wei-Hwa Huang has found at least five
solutions for all the positions he's checked.
Gary Mulkey has solved the Cairo problem of Mark
Thompson. I've put his findings here.
material added august 1st
I regularly check the websites of Zucca,
Clarke for polyform
discoveries. Livio and Brendan Owens recently made a list of the
17 tetracairos. It's a rather nice set!
The 17 tetracairos. Larger Image.
Livio called them polycairos after the famous Cairo tessellation of equilateral
pentagons. I tried to solve the lovely figure in black for awhile.
Eventually, I pulled out the awesome tool known as Parity,
and noticed it was impossible. Do you see why? The four free
pentagons can be grouped together in five different ways, in theory.
It was a lovely enough set to play with that I'm having 54 sets cut.
If you'd like to order one, see my orders
page. I'll be selling my first sets while I'm in Los Angeles
Aug 10-Aug14 for a puzzle convention. Here,
you can see Livio's list of the 55
Brendan Owens shows how 16 tetracairos make a diamond.
The person at the forefront of Cairo puzzles is Mark Thompson.
He discovered the tetracairos several years ago. A small puzzle of
his -- Arrange the 5 tricairos into a shape with perimeter 21. At
website, you can see several puzzles and games based on this tiling
pattern. He recently gave the same set as above to Kate Jones of
Enterprises (the best place to get high quality puzzles). His
game looks like an excellent puzzle. Can these 32 tiles be placed
to completely match up? I also found his Venn
Polyominoes page intriguing.