382] 
NOTE ON THE TETRAHEDRON. 
559 
Or it may be constructed even more simply as follows : viz. if AB'CD' and 
A'BG'D be parallel faces of any rectangular parallelopiped (the angles A and A', 
B and B', G and C, D and D' being respectively opposite to each other), then ABGD 
or A'B'G'D' is a tetrahedron of the form in question. The consideration of the 
rectangular parallelopiped puts in evidence the foregoing geometrical property. 
In such a tetrahedron the line joining the centres of a pair of opposite sides 
is in the language of Bravais, see his “ Mémoire sur les polyèdres de forme symétrique,” 
Liouville, t. xiv. (1849), pp. 141—180, a binary axis of symmetry: viz. the figure is 
not altered by turning it round such axis through an angle = ^360°. There are thus 
three such axes at right angles to each other, but the figure has not any centre of 
symmetry, nor (assuming that it is not further particularised) any plane of symmetry : 
each of the three axes is a principal axis, and the figure belongs to the sixth of 
Bravais’ twenty-three classes of polyhedra, see the table p. 179. It was in fact by 
seeking to construct a figure of this class that I was led to the investigation.