242] SECOND NOTE ON POINSOT’s FOUR NEW REGULAR POLYHEDRA. 87 
polyhedra. I remark that, in the equation S+H=A+1, II should, in analogy with 
Cauchy’s notation for polyhedra, be replaced by P; so that we have for a single polygon, 
A=S] 
and for the partitions of a polygon, 
A = S + P-1 : 
corresponding respectively to Euler’s theorem for a single polyhedron, viz. 
S + H=A + 2; 
and to Cauchy’s theorem for the partitions of a polyhedron, viz. 
£ + tf = ^ + 2 + (P-l). 
Cauchy’s second memoir (pp. 87—98) contains a very beautiful demonstration of 
the theorem implied in the ninth definition of the eleventh book of Euclid, viz. that 
two convex polyhedra are equal when they are bounded by the same number of faces 
equal each to each. 
2, Stone Buildings, W.G., February 1, 1859.