"318 DUNCAN MCLAREN YOUNG SOMMERVILLE.

for the five corresponding types in four dimensions. The honeycomb 435,for instance, consists of an infinite net of regular hexahedra (containing

Jour regular plane quadrilaterals meeting by threes at each vertex) such thatjive hexahedra have one edge in common. This is possible since in hyper-bolic space a cube has acute dihedral angles. Such ideas have had anunexpected application to the theory of abstract groups.

His familiarity with non-Euclidean geometry must have been almostunique: he treated it as worthy of a detailed study comparable to thataccorded to Euclidean geometry. Other examples of his researchesinclude the classification of all types of non-Euclidean geometry, themeasurement of generalized angles in higher space, and Eulers theorem•on polyhedra. His wide knowledge of geometry (and incidentally ofEuropean languages) is seen most clearly in his Bibliography of non-Euclidean geometry, which includes far more than its title suggests.

Sommerville was ever ready to apply his special gifts to unusual•examples, as in his analysis of preferential voting by means of a figure inhigher space, and in an original analysis of the musical scale. His was aJife of unsparing activity, and the fruits of his work will abide.

CORRIGENDUM

ABSTRACT GROUPS OF THE FORM F / = F / = (F,-F;)!= 1*.

H . S. M. COXETEK.

P. 218, line 6. The regular polytope \k, 3"-'} is finite (a) when n = 1, (6) when k ^ 4,. (c) when k — 5f n — 2 or 3.

* Journal London Math. Soc, 9 (1934), 213-219.