The fourth dimension

126 THE FOURTH DIMENSION

could be taken out of the cube and placed on a plane.

It is a figure which will fill a plane by equal repetitions of itself. The plane being representing this construction in his plane would take three squares to represent the cube. Let us suppose that he takes the 4 axes in his space and i represents the axis running out

Fig. v7, of his space, fig. 68. In each of the three squares shown here as drawn separately he could select the points given by the rule, and he would

A D, -D 402 O12 201 102 K 210 20 S

Fig. 68,

then have to try to discover the figure determined by the three lines drawn. The line from 210 to 120 is given in the figure, but the line from 201 to 102 or Gx is not given. He can determine Gk by making another set of drawings and discovering in them what the relation between these two extremities is,

102 102 02) 20) A C, 120 B 210

Fig. 69,

Let him draw the 7 and & axes in his plane, fig. 69. The 7 axis then runs out and he has the accompanying figure. In the first of these three squares, fig. 69, he can