VIlJ 



OF HKXAIJONAL PATTERNS 



511 



Fig. 189. 



A diatom. Triccrniiinn sj).. shewing j)attern of hrxagoiis; 

 (). Prochnow, foDnenkunst der Xatur. 



y'.HH). From 



a zone of twelve, and around these a zone of eighteen, and so on. 

 total number, excluding the central hexagon, is accordingly: 



And the 



For one zone 

 „ two zones 

 ,, three zones 

 „ four zones 

 „ five zones 



6=3x1x2=6x1 

 18 2x3 3 



36 3x4 6 



60 4x5 10 



90 5x6 15 



and so forth. If N be the number of zones, and if we add one to the above 

 numbers for the odd central hexagon, then the rule is that the total number 

 H = 3N (A' + l) + l. Thus, if in a preparation of a fly's cornea I can count 



