Ball, W. W. Rouse (Walter William Rouse), 1850-1925 · London, Macmillan · leaf 78
instance the accompanying figure, representing a closed network in three dimensions of 15 lines formed by the sides of two pentagons and the lines joining their corresponding angular points, cannot be coloured as described by Tait. If the figure is in three dimensions, the lines intersect only at… … the lines is not regarded as such a vertex. Expressed in tech- nical language the difficulty is this. Petersen* has shown that a graph (or network) of the 2nth order and third degree and without offshoots (or feutlles) can be resolved into three graphs of the 2nth order and each of the first…
