478 ON CONCRETIONS, SPICULES, ETC. [ch. ix 



another class in a simpler aggregate of a few, otherwise isolated, 

 vesicles. But among the vast number of other known Radiolaria, 

 there are certain forms (especially among the Phaeodaria and 

 Acantharia) which display a still more remarkable symmetry, the 

 origin of which is by no means clear, though surface-tension 

 doubtless plays a part in its causation. These are cases in which 

 (as in some of those already described) the skeleton consists 

 (1) of radiating spicular rods, definite in number and position, 

 and (2) of interconnecting rods or plates, tangential to the more 

 or less spherical body of the organism, whose form becomes, 

 accordingly, that of a geometric, polyhedral solid. It may be 

 that there is no mathematical difference, save one of degree, 

 between such a hexagonal polyhedron as we have seen in Aula- 

 caniha, and those which we are about to describe ; but the greater 

 regularity, the numerical symmetry, and the apparent simpHcity 

 of these latter, makes of them a class apart, and suggests problems 

 which have not been solved nor even investigated. 



The matter is sufficiently illustrated by the accompanying 

 figures, all drawn from Haeckel's Monograph of the Challenger 

 Radiolaria*. In one of these we see a regular octahedron, in 

 another a regular, or pentagonal dodecahedron, in a third a regular 

 icosahedron. In all cases the figure appears to be perfectly 

 symmetrical, though neither the triangular facets of the octahedron 

 and icosahedron, nor the pentagonal facets of the dodecahedron, 

 are necessarily plane surfaces. In all of these cases, the radial 

 spicules correspond to the solid angles of the figure ; and they are, 

 accordingly, six in number in the octahedron, twenty in the 

 dodecahedron, and twelve in the icosahedron. If we add to these 

 three figures the regular tetrahedron, which we have had frequent 

 occasion to study, and the cube (which is represented, at least 

 in outline, in the skeleton of the hexactinellid sponges), we have 

 completed the series of the five regular polyhedra known to 

 oleometers, the Platonic bodies f of the older mathematicians. It 

 is at first sight all the more remarkable that we should here meet 



* Of the many thousand figures in the hundred and forty plates of this beautifully 

 illustrated book, there is scarcely one which does not depict, now patently, now 

 in pregnant suggestion, some subtle and elegant geometrical configuration. 



"f They were known (of course) long before Plato: nXdrui' 8i Kai kv toijtois 



TTudayopl^ei. 



