TORRE. 
Vol. 31 September-October No. 5 
Modelling the orthic tetrakaidecahedron 
Epwin B. MATZKE 
One of the most fascinating pages in the history of science is 
that which relates the discovery of the planet Neptune. After 
long and involved mathematical computations, Adams in Eng- 
land and Leverrier in France explained the movement of Uranus 
by the existence of a previously unknown planet, and they de- 
termined its approximate position. On the basis of Leverrier’s 
calculations, Galle, in Berlin, was able almost immediately to 
locate the new planet. 
Less spectacular, perhaps, less heralded, but no less scien- 
tific has been the investigation of cell shapes in the organic 
world by Kelvin and Lewis. As far back as 1887 Kelvin pub- 
lished an essay ‘‘On the division of space with minimum parti- 
tional area,” in which he described a fourteen-sided figure that 
he called a tetrakaidecahedron. A similar figure had been known 
to the crystallographers even before Kelvin’s publication. In 
contrast to the search for Neptune, which went on with almost 
feverish haste after the supposed orbit had been approximately 
determined, Kelvin’s suggestion lay fallow for thirty-six years; 
it was only in 1923 that Lewis showed that cells of elder pith 
tend to be fourteen-sided, and at times show an alternation of 
hexagonal and square faces suggestive of Kelvin’s figure. Lewis 
(1925, 1928) has since extended his observations, and gives data 
showing the primarily tetrakaidecahedral form of such diverse 
tissues as the stellate cells of Juncus, cells of human adipose and 
oral epithelial tissues, and cork cells, while Hein (1930 a, b) 
comes to similar conclusions in studying sclerotial tissue of the 
fungi. From a mathematical standpoint the orthic tetrakaideca- 
oy has been considered in a previous publication (Matzke 
27). i 
Kelvin apparently arrived at his tetrakaidecahedron from 
studying the cubic skeleton frame of Plateau (1873). This ey 1 
Produced in figure 1—the frame being shown by the heavy lines. 
129 
