Polysexes
This page is an attempt to generalize the concept which inspired the Sexominoes, the SexeHexeS, the Xominoes and the Zucca's Puzzle.
Among the regular polygons, the triangles, the squares and the hexagons tile the plain. I introduced conditions between contiguous edges. The condition could be: sex as the SexeHexeS and the Sexominoes, a more complex function as the Xominoes, drafters as Zucca's Puzzle. But also it could be different colors, mechanical keys, magnetic fields, electronic valences, human likes and dislikes...
Each piece has a barycenter, sometime not a true barycenter, but a point of rotation which can be placed on a grid: a hexagonal grid if the pieces are triangles, a square grid if the pieces are squares, a triangular grid if the pieces are hexagonal.
The possible pieces are a subset of:
This number includes the rotations which you must eliminate, if you want 1side different pieces only. You must eliminate the mirror pieces yet, if you want 2side different pieces only.
The condition could be:
If the conditions are simple, we could attempt a classification. Below there are the numbers of different pieces:
Nr.
edgeforms 
TRIANGLE
1SIDE 
TRIANGLE
2SIDE 
SQUARE
1SIDE 
SQUARE
2SIDE 
HEXAGON
1SIDE 
HEXAGON
2SIDE 
1  1  1  1  1  1  1 
2  4  4  6  6  14  13 
3  11  10  24*  21  130**  92** 
4  24  20  70  55  700  430 
5  45  35  165***  120  ...  ... 
6  76  56  336  231  ...  ... 
7  119  84  616  406  ...  ... 
8  176  120  1044  666****  ...  ... 
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New examplesBiblical or Fourier's Puzzle
666 pieces = 37x18 rectangle with sinusoidal edge (odd armonics).
Do you remember the Fourier Series?
sin(x)+sin(3x)/3+sin(5x)/5+sin(7x)/7+...
generates a square wave!
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Faces Puzzle
90 2side pieces = 10x9 rectangle. This simple puzzle has "complex" conditions.
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If you have an interest in the mathematical aspect of the puzzles, read this interesting email from Chris Hartman.
If you like, send me an email here.
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A note
Many centuries ago, perhaps in Mesopotamia, the ancient Arabs invented a two squares based game, with seven contiguous conditions: it is the Domino.
Oh! It's an idea!
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I think that many molecules and many crystals are similar puzzles. It's naturally possible to apply the concept to 3dimension or ndimension space, but this will be an other page.
1st edition: 14 Apr 2000

POLYSEXES 
Sexominoes 
Xominoes 
SexeHexeS 
More about SexeHexeS 
How we did it 
Other Sexehex Puzzle 
Chronicle 
My Solution 
Zucca's Puzzle 
Domino Puzzle 
 Pentominoes  More about pentominoes  The cube  3D pentominoes  Fibonacci Machine  Download  Links 