[Illustration: Fig. 131. Surface-views of Corals with undeveloped thecae and confluent septa. A, _Thamnastraea_; B, _Comoseris_. (From Nicholson, after Zittel.)] ―――――――――― The most famous of all hexagonal conformations and perhaps the most beautiful is that of the bee’s cell. Here we have, as in our last examples, a series of equal cylinders, compressed by symmetrical forces into regular hexagonal prisms. But in this case we have two rows of such cylinders, set opposite to one another, end to end; and we have accordingly to consider also the conformation of their ends. We may suppose our original cylindrical cells to have spherical ends, which is their normal and symmetrical mode of termination; and, for closest packing, it is obvious that the end of any one cylinder will touch, and fit in between, the ends of three cylinders in the opposite row. It is just as when we pile round-shot in a heap; each sphere that we {328} set down fits into its nest between three others, and the four form a regular tetrahedral arrangement. Just as it was obvious, then, that by mutual pressure from the six _laterally_ adjacent cells, any one cell would be squeezed into a hexagonal prism, so is it also obvious that, by mutual pressure against the three _terminal_ neighbours, the end of any one cell will be compressed into a solid trihedral angle whose edges will meet, as in the analogous case already described of a system of soap-bubbles, at a plane angle of 109° and so many minutes and seconds. What we have to comprehend, then, is how the _six_ sides of the cell are to be combined with its _three_ terminal facets. This is done by bevelling off three alternate angles of the prism, in a uniform manner, until we have tapered the prism to a point; and by so doing, we evidently produce three _rhombic_ surfaces, each of which is double of the triangle formed by joining the apex to the three untouched angles of the prism. If we experiment, not with cylinders, but with spheres, if for instance we pile together a mass of bread-pills (or pills of plasticine), and then submit the whole to a uniform pressure, it is obvious that each ball (like the seeds in a pomegranate, as Kepler said), will be in contact with _twelve_ others,—six in its own plane, three below and three above, and in compression it will therefore develop twelve plane surfaces. It will in short repeat, above and below, the conditions to which the bee’s cell is subject at one end only; and, since the sphere is symmetrically situated towards its neighbours on all sides, it follows that the twelve plane sides to which its surface has been reduced will be all similar, equal and similarly situated. Moreover, since we have produced this result by squeezing our original spheres close together, it is evident that the bodies so formed completely fill space. The regular solid which fulfils all these conditions is the _rhombic dodecahedron_. The bee’s cell,