130 
If this frame is dipped into a soap solution and then withdrawn, 
the soap films form a quadrilateral face in the center, and each 
of the four sides of the quadrilateral also forms a side of a half- 
hexagon. This relationship is similar to a quadrilateral face of 
Kelvin’s tetrakaidecahedron, which is surrounded by four hex- 
agonal faces (as shown in figure 3). The limits of the three half- 
hexagons of figure 1 are represented by dotted lines in figure 3. 
The region enclosed by the dotted lines in figure 3 thus corre- 
sponds to the dotted portion of figure 1. Kelvin objected to the 
rhombic dodecahedron as a form for the partitioning of space 
ae 
l! I 
AN X 
f. Tag 
Zz x 
1 
GURE 1. Cubic skeleton frame of Plateau with soap films, a quadri- 
lateral face and four half-hexagonal faces of Figure 3 shown by dotted 
lines 
FIGURE 2. Skeleton frame of a rectangular prism, to show the slipping 
of the soap films; it should be removed from the soap solution as. indicated 
by the arrow. 
because of its tetrahedral angles which, as he said, are essenti- 
ally unstable. By blowing gently on the edge of the quadri- 
lateral face in figure 1, that is by blowing parallel with its sur- 
face, that face will decrease in size, one side of the half-hexagonal 
faces (which are also quadrilaterals) thus becoming smaller and 
smaller. However, as Kelvin pointed out, this quadrilateral 
face cannot be made to disappear completely, for just as it ap- 
proaches the vanishing point there is a readjustment of the soap 
films, and a new quadrilateral face is formed, its surface being 
perpendicular to the surface of the first. 
A similar slipping or readjustment of the soap films can be 
demonstrated by using instead of the cubic skeleton frame, the 
