( 552 ) 
A’, B’,C’; of these C, D, N coincide respectively with NW’, A’, BY). 
ooh, ake 
ase —,—<:— |}. Hae ids ee forms ( ) : 
Case i= Te = ach En the three forms (14, 21, 9), (26, 39,15), 
EL 
i ; 0 ; : : 
(32, 48,18) with the fractions 16°16’ 16 oe in two oppositely orien- 
. . . . 5 
tated positions. The shape of the faces proves that two polyhedra & 
in contact must have an isosceles trapezium in common and two 
7 
16}? hexagon of the equatorial belt, whilst the required 
parallelism of all the axes J/N only allows the possibility of two 
polyhedra 
3 E 5 
polyhedra & having a hexagon, and two polyhedra & having 
a hexagon of the equatorial belt in common. Moreover the contact 
5 7 
of a polyhedron Ga) and a polyhedron (= must find place in 
7 
an equatorial hexagon, that of the forms (=) and (5) in a deltoid, 
3 5 
whilst the forms (5) and (= may be in contact by a hexagon. 
From all this may be easily deduced that the projection of the 
space-filling on a plane normal to the axes (fig. 7°) consists in the 
superposition of two plane-fillings, of which the one brought to the 
5) 
fore here contains equatorial sections of the polyhedra € and 
4 
D ; 3 
— |, whilst the more regular one of hexagons, the vertices of 
16 
which coincide with the centres of the polygons of the former, is 
built up of equatorial sections of the polyhedron This proves 
3 
at the same time that no two polyhedra & are in facial contact, 
: 9 : 
neither that two polyhedra (5) have a hexagon in common. 
The projection on an axis is represented in fig. 8’ in three layers, 
7 5 3 
successively related to the polyhedra (5) (5): (se): In none 
of the three layers do these axes cover the line of projection entirely. 
In the manner explained above have been indicated on MN the 
projections A, B,..., H, on M'N' the projections A’, B’,..., #5 
1) These points have been indicated by the same letters on the polyhedra 
11 
5 and ze of the second part of plate Il; but here the daslies 
have been omitted. 
corresponding to 
