92 REV. T, P. KIRKMAN ON THE 
V.— On the general solution of the problem of the poly- 
edra. By the Ruv. Tuo. P. Kirxman, M.A., F.R.S., 
Rector of Croft with Southworth, and Honorary 
Member of the Literary and Philosophical Society of 
Manchester. 
Read January 26th, 1858. 
Lone as the question -— How many #-edra are there? — 
has been before the mathematical world, no method has 
hitherto been discovered, except that of tentative con- 
struction, whereby the number required can be completely 
assigned even for v=8. ll that has been effected, so far 
as I can learn, towards the solution of the problem by 
general methods, may be seen in four memoirs of mine 
printed in the Philosophical Transactions for 1856 and 
1857, and in a later memoir “On the partitions of the 
y-pyramid,” of which some account is given in the Pro- 
ceedings of the Royal Society for 1857,* and in another 
“‘On the triedral partitions of the 7-ace” in the Manchester 
Memoirs for 1857. In these papers are discussed certain 
great classes of the x-edra. In the pages following is 
made the first attempt at the analysis and solution of the 
whole problem. 
It is known that if the Q’ faces of p’-acral Q’-edron be 
an A-gon, a B-gon---a Q-gon, and its p’ summits an a- 
* This memoir is now printed in the Philosophical Transactions. 
