4 
“ The problem of the enumeration of the polyhedra is one 
of extreme difficulty, and I am not aware that it has been dis- 
cussed elsewhere than in Mr. Kirkman’s valuable series of 
papers on this subject in the Memoirs of this Society, and in 
the Philosophical Transactions. A case of the general problem 
is that of the enumeration of the polyhedra with trihedral 
summits; and Mr. Kirkman, in the earliest of his papers, viz., 
that c On the Representation and Enumeration of Polyhedra ’ 
(Mem. Vol. XII., pp. 47, 70, 1855), has in fact, by an 
examination of the particular case, accomplished the enumera- 
tion of the octahedra with trihedral summits. 
“ It is intended, in the present paper, to give a method for 
the derivation of the triangular-faced polyacrons of a given 
number of summits from those of the next inferior number of 
summits, and to exemplify it by finding, in an orderly manner, 
the triangular-faced polyacrons up to the octacrons ; thus, as 
regards the examples, stopping at the same point as Mr. 
Kirkman ; for although perfectly practicable, it would be very 
tedious, and there would be no commensurate advantage to 
carry them further.” 
At this, the first Meeting of the Session, a large number 
of books, chiefly Transactions of learned Societies abroad, 
were laid on the table. The Chairman congratulated the 
Society on the rapid increase of its Library, which was mainly 
owing to the great ability and zeal of Mr. Ekman, the 
Honorary Librarian. 
