5906 Scientific Proceedings, Royal Dublin Society. 
Case of trapezohedral tetartohedrism. 
Tf the radii of two sets of equal spheres are in a certain ratio, 
we are able to build them together into a very closely-packed homo- 
geneous assemblage of the type numbered 52 in my list,’ whose 
axes and coincidence-movements are those of system 22 of Sohncke. 
The arrangement of the centres of the two sets of spheres is diffi- 
cult to indicate on a diagram; the larger have their centres on 
digonal axes, and are therefore half as numerous as the smaller 
ones. Hach larger sphere is in contact, or nearly in contact, with 
fourteen surrounding spheres, each smaller one nearly in contact 
with ten.2 The generic symmetry is that of class 15 in Sohncke’s 
list of Krystallklassen. The 
two kinds are present in the 
numerical proportions 1 : 2 and 
the centres of the less numer- 
ous form a singular point-sys- 
tem. 
The balls may be all un- 
linked, or they may, consis- 
tently with the symmetry, be 
linked together to form similar 
groups of three, one of one kind 
and two of the other. If they 
are thus linked a slightly modi- 
fied arrangement will be ap- 
propriate, and groups of three 
interpenetrating spheres,* two of one size and the third of 
another, will be used to build up the type of symmetry. An 
arrangement of the sphere centres such as may be presented in 
this case is depicted in fig. 12, the methods employed by Sohncke 
1 Zeitschr. fiir Kryst., 23, p. 32. 
2 For the reason stated in a previous example, the centres of the spheres do not 
precisely give a possible equilibrium arrangement for particles of two kinds, but a 
slight modification of the arrangement of the sphere-centres which does not alter the 
type of symmetry, would appear to satisfy the necessities of statical equilibrium and 
give a possible arrangement. 
3 Compare p. 530. 
