598 THE FORMS OF TISSUES [ch. 



A B C D 



aac 222 33 44 6 8-5 



aca 222 33 44 6 8-5 



I 



9 

 k 



Nine cells may be arranged in twenty-seven ways. In higher 

 series the numbers increase very rapidly, but the cells will tend to 

 overlap, and so introduce a new complication* 



We may draw help from the theory of polyhedra (in an elementary, 

 way) if we treat our group of eight cells (none of them "insular") 

 as part of a polyhedron, to be completed by one eight-sided cell, 



* Max Bruckner states the number of possible arrangements of thirteen cells, 

 with trihedral junctions, as nearly 50,000; of sixteen, nearly 30 miUions; and of 

 eighteen, "bereits iiber einige Billionen" (Proc. Math. Congress, Bologna, 1930, vol. 

 IV, p. 11), It is plain that the study of " cell-lineage," or the mapping out in detail 

 of the cell-arrangements after repeated cell-divisions, is only possible under severe 

 limitations. 



