552 THE FORMS OF TISSUES [ch. 



curved " anticlastic " surfaces;- and these latter have at every point 

 equal and opposite curvatures, and are surfaces of minimal curvature 

 for a boundary of six curved edges. This figure has the remarkable 

 property that, hke the plane rhombic dodecahedron, it so partitions 

 space that three faces meeting in an edge do so everywhere at 

 co-equal angles of 120°; and, unlike the rhombic dodecahedron, 

 four edges meet in each point or corner at co-equal angles of 

 109° 28'*. 



We may take it as certain tha^), in a homogeneous system of fluid 

 films Hke the interior of a froth of soap-bubbles, where the films 

 are perfectly free to glide or turn over one another and are of 

 approximately co-equal size, the mass is actually divided into cells 

 of this remarkable conformation: and the possibility of such a 

 configuration being present even in the cells of an ordinary vegetable 

 pareilchyma was suggested in the first edition of this book. It is 

 all a question of restraint, of degrees of mobihty or fluidity. If we 

 squeeze a mass of clay pellets together, hke Buffon's peas, they come 

 out, or all the inner ones do, in neat garnet-shape, or rhombic 

 dodecahedra. But a young student once shewed me (in Yale) that 

 if you wet these clay pellets thoroughly, so that they slide easily 

 on one another and so acquire a sort of pseudo-fluidity in the mass, 

 they no longer come out as regular dodecahedra, but with square 

 and , hexagonal facets recognisable as those of ill-formed or half- 

 formed tetrakaidekahedra. 



Dr F. T. Lewis has made a long and careful study of various 

 vegetable parenchymas, by simple maceration, wax-plate recon- 



* Von Fedorov/ had already described (in Russian), unaware that Archimedes 

 had done so, the same figure under the name of cubo-octahedron, or hepta- 

 parallelohedron^ hmited however to the case where all the faces are plane and 

 regular. This cubo-octahedron, together with the cube, the hexagonal prism, 

 the rhombic dodecahedron and the "elongated dodecahedron," constitute the 

 five plane-faced, parallel-sided figures by which space is capable of being completely 

 filled and uniformly partitioned; the series so forming the foundation of Von 

 Fedorow's theory of crystalline structure — though the space-fillers are not all, and 

 cannot all be, crystalline forms. All of these figures, save the hexagonal prism, 

 are related to and derivable from the cube, so we end by recognising two principal 

 types, cubic and hexagonal. We have learned to recognise the dodecahedron, 

 and we may find in still closer packing the cubo-octahedron, in a parenchyma; 

 the elongated dodecahedron is, essentially, the figure of the bee's cell; the cube 

 we have, in essence, in cambium -tissue; the hexagonal prism, dwarf or tall, simple 

 or recognisably deformed, we see in every epithelium. 



