THE SHAPE OF CELLS. 549 



The smallest cell observed, having a volume in the model of 10 c.c, 

 was so very small and flattened that it required special examination 

 to be sure it was not a distended intercellular space. That possibility 

 could be definitely excluded. The model seems a formless body 

 (Figure 19) yet one which may be tentatively explained as due to an 

 unequal vertical division of a tetrakaidecahedron. The fragment of 

 the pattern-model shown in Figure IS has seven surfaces, but the 

 actual cell in Figure 19 has but six. Four of these can be seen in the 

 figure. The others are a very small triangular facet at the top of the 

 hidden side, and a broad pentagonal area covering the remainder of 

 that side. If the contact x in the pattern should be eliminated, there 

 would remain six surfaces, each of which would have the number of 

 sides actually found in the hexahedral cell. 



Eleven of the forty-two cells modeled have now been considered, 

 and it has been shown that great variations in the number, shape and 

 arrangement of their facets are entirely consistent with a typical 

 tetrakaidecahedral form. An equal division of a tetrakaidecahedron 

 produces cells with only eleven surfaces; an unequal division may 

 reduce the number still further, to eight or even seven, as has been 

 shown by examples. On the other hand, if all the cells surrounding a 

 particular tetrakaidecahedral cell should divide transversely, the 

 undivided central cell would have three tiers of lateral surfaces and 

 twenty contacts, the top and base remaining hexagonal. A cell among 

 those modeled which closely approximates this form was evidently 

 produced by a vertical division at a time when the cells around it 

 divided transversely. If all the cells surrounding a particular cell, 

 except the one immediately above it and the one immediately below it, 

 should divide in halves vertically, and all in one plane passing through 

 the sides and not the angles of the top and basal surfaces, then the 

 central cell would be octagonal above and below; it would have six- 

 teen lateral surfaces arranged in two tiers, — eighteen surfaces alto- 

 gether; and there would be two points, on opposite sides of the cell, 

 where four surfaces would meet, producing unstable tetrahedral angles. 

 Such tetrahedral angles, made by the vertical bisection of a quadri- 

 lateral and of the hexagon above or below it as the case may be, would 

 be the meeting place of two quadrilaterals side by side and two penta- 

 gons side by side, and precisely this grouping is seen in one of the 

 models, in which the four surfaces meet at a salient point. Another 

 model, being that of the largest cell studied, illustrates the entire con- 

 figuration under discussion. Its upper surface is octagonal, and the 

 two added borders are clearly the result of the bisection of two oppo- 



