perfect dodecahedrons, the incidence would necessarily be 120°. Supposing the macles represented by fig. 188, pl. 24, or fig. 208, pl. 25, to consist of four sections similar to fig. 196, the plane that would be given to the upper and lower faces by a horizontal section, would resemble fig. 202, the angles of which are 112°. 10′, and it will be obvious that this figure could not be made to agree with the plane of section of the perfect dodecahedron fig. 107, the angles of which are 120°, by adding to it triangles of a similar description.
The figures in this series occupying pl. 26, are extremely complex, as except the latter, each consists of four, or a greater number of similar parts of some one of the macles already described, for which reason I have termed them macles of macles.
That which is described by fig. 222, Pl. 26, consists of four similar parts of macles, fig. 188, Pl. 24, which by fig. 223, Pl. 26, is placed in such a position as to shew that section of fig. 188, which forms one-fourth part of fig. 222, as will be readily seen by noticing the figures 1, 1, on each, the planes on which they are placed, being those of the first modification, or in other words, of the common prism. The striæ on these macles uniformly take the direction given by the lines on fig. 222. I have several that shew both terminations, and the natural joints of the four portions of which they are constituted are always visible on the direction of the stronger lines down the center of the faces of what may be termed the prism of the macle. As the incidence of the planes 1, on 1 of this macle, give by the common goniometer exactly 90°, it follows that a horizontal section of this macle would give a square plane to each part so divided, Let this plane be represented by fig. 224,