66 



GEOMETRICAL RECREATIONS 



[CH. IV 



spaces of the accompanying diagram. In these fundamental 

 forms A represents one colour and B the other colour. The 

 diamond-shaped figure in the middle of the diagram represents 

 an anallagmatic pavement of 256 tiles which is symmetrical 

 about its diagonals. In half the rows and half the columns 

 each line has 10 white tiles and 6 black tiles, and in the 

 remaining rows and columns each line has 6 white tiles and 



An Anallagmatic Isochromatic Pavement. 



10 black tiles. Such an arrangement, where the difference 

 between the number of white and black tiles used in each line 

 is constant, and equal to Vm, is called isochromatic. If m is 

 odd or oddly even, it is impossible to construct anallagmatic 

 boards which are isochromatic. 



Interesting problems can also be proposed when the tiles are 

 triangular, whether equilateral or isosceles right-angled. Two 

 equal isosceles right-angled tiles of different colours can be 



