VII] OF THE TETRAKAIDEKAHEDRON 551 



within the old, and set it in place of the former fenestra. The inner 

 polyhedral bubble so produced may be of any dimensions, but it 

 resembles the outer polyhedral cage precisely, except in the 

 curvature of its sides ; it has all its faces spherical, and all of equal 

 radius of curvature; its edges are either arcs of circles or straight 

 lines. Later on, we shall see that there is no small biological 

 interest attaching to these configurations. 



Lord Kelvin made the remarkable discovery that the square 

 fenestra with the four quadrilateral films impinging on its sides, in 

 Plateau's experiment, represented the one-sixth part of a symmetrical 

 figure; that this figure when complete was bounded by six squares 

 and eight hexagons; that by means of an assemblage of these 



Fig. 213. A set of 14-he(lra, to shew close-packing. From F. T. Lewis 



fourteen-sided figures, or "tetrakaidekahedra," space is filled and 

 homogeneously partitioned — into equal, similar and similarly situated 

 cells — with an economy of surface in relation to volume even greater 

 than in an assemblage of rhombic dodecahedra*. 



The tetrakaidekahedron, in its most generalised case, is bounded 

 by three pairs of equal and opposite quadrilateral faces, and four 

 pairs of equal and opposite hexagonal faces, neither the quadri- 

 laterals nor the hexagons being necessarily plane. In its simplest 

 case, with all its facets plane and equilateral, it is Kelvin's "ortho- 

 tetrakaidekahedron " ; and also (though Kelvin was unaware of the 

 fact) one of the thirteen semi-regular and isogonal polyhedra, or 

 "Archimedean bodies." In a particular case, the quadrilaterals are 

 plane surfaces with curved edges, but the hexagons are slightly 



* Kelvin, Boyle Lecture and Baltitnore Lectures. In the first of these Kelvin 

 described the plane-faced tetrakaidekahedron; in the second he shewed how that 

 figure must have its faces warped and edges curved to fulfil all the conditions of 

 minimal area. 



