550 THE FORMS OF TISSUES [ch. 



symmetry of the figure, to which side of the skeleton cube the 

 square lies parallel; wherever it may be, if we blow gently on it, 

 then (as M. Van Rees discovered) it alters its place and sets itself 

 parallel now to one and now to another of the paired faces of the 

 cube. 



The skeleton cube, Hke the tetrahedron which we have already 

 studied, is only one of many interesting cases; for we may vary 

 the shape of our wire cages and obtain other and not less beautiful 

 configurations. An hexagonal prism, if its sides be square or nearly 

 so, gives us six vertical triangular films, whose apices meet the 

 corners of a horizontal hexagon*; also six pairs of truncated 

 triangles, which link the top and bottom edges of the cage to the 

 sides of the median hexagon. But if the height of the hexagonal 

 prism be increased, the six vertical films become curvihnear triangles, 

 with sides concave towards the apex; and the twelve remaining 

 films, which spring from the top and bottom of the hexagon, are 

 curved surfaces, looking like a sort of hexagonal hourglass f. 



There is a deal of elegant geometry in these various configurations. 

 Lamarle shewed that if, in a figure represented by our wire cage, 

 we suppress (in imagination) one face and all the other faces 

 adjoining it, then the faces which remain are those which appear 

 in the centre of the figure after the cage has been withdrawn from 

 the soap-solution. Thus, in a cube, we suppress one face and the 

 four adjacent to it; only one remains, and it reappears as the central 

 square in the middle of the new configuration; in the tetrahedron, 

 when we have suppressed one face and the three adjacent to it, 

 there is nothing left — save, a median point, corresponding to the 

 opposite corner. In a regular dodecahedron, if we suppress one 

 pentagonal face and its five neighbours, the other half of the whole 

 figure remains; and the dodecahedral cage, after immersion in the 

 soap, shews a central and symmetrical group of six pentagons J. 



Moreover, while the cage is carrying its configuration of films, 

 we may blow a bubble within it, and so insert a new polyhedron 



* The angles of a hexagon are too big, as those of a square were too small, to 

 form the Maraldi angles of symmetry; hence the sides of the hexagon are found 

 to be concave, as those of the square bulged out convexly. 



t Cf. Dewar, op. cit. 1918. 



X That is to say, if nF„^ be a polyhedron (of n m-faced sides), the corresponding 

 wire cage will exhibit (w - m + 1) i^^ as central fenestrae. 



