716 Proceedings of Royal Society of Edinburgh. [sess. 
fig. 5, which also is taken from Mr Barlow’s paper. "We thus get 
eight equilateral triangular facets, each showing close triangular 
grouping of the globes appearing in it. The four pairs of planes of 
these facets are, of course, parallel to the four faces of the tetra- 
hedron, ABCD. If we make the bevelling of each corner deep 
enough, nothing is left of the cube but a regular octohedron, whose 
eight faces are parallel to the eight faces of the tetrahedron. 
§ 55. If in building a triangular pyramid we commence with 
globes in close triangular order on a horizontal plane, and place the 
second layer above it over the white dots ( ° ) of the diagram (fig. 6), 
the third layer over the inner triangle of black dots ( • ), and the 
fourth a single globe over the centre of the diagram, we build up 
precisely the portion bevelled off the primitive cube in § 54. Thus 
we have a triangular pyramid whose three sides are isosceles right- 
angled triangles meeting at right angles along the three slant edges. 
The globes in these three faces are in square order. The lines of 
globes in contact in these faces are parallel and perpendicular to the 
bounding edges of the base. In the pyramid corresponding to the 
actual diagram, or any other with an odd number of globes in each 
