. 128. OF THE CONNEXION OF FORMS. 135 



the number which denotes the variety of these forms, as 

 contained in the preceding paragraphs 71-77* 



. 128. RESOLUTION OF FORMS BELONGING TO THE 

 FIRST DEGREE OF REGULARITY. 



To resolve a form of several axes, means to pro- 

 duce from it two or more equal and similar forms 

 of several axes, the faces of which agree in num- 

 ber and situation with one-half or one-fourth of the 

 faces of the original form. These forms reproduce 

 the original one, if combined in the required po* 

 sition. 



A form of several axes, produced by the resolution of an- 

 other, if it contains half the number of its faces, is termed 

 a Half; if it contains only one-fourth of the faces, it is 

 termed a Fourth of the resolved or original form. 



Those halves must not be taken for half forms, or such 

 as might be obtained by cutting in two, one of the original 

 forms, as would be a simple pyramid. Nor are the fourths 

 real quarters of original forms, because they have not been 

 obtained by cutting in two, one of the preceding halves. 



The method by which the resolution is effected, is the 

 following : 



Place the given form in an upright position, so as to 

 make one of its rhombohedral axes vertical. 



Call the upper terminal point of this axis a Principal 

 Point, the lower one a Subordinate Point, and transfer those 

 names to all the terminal points of rhombohedral axes, dis- 

 tant from the vertical one, for 109 28' 16". In the hexa- 

 hedron, as represented Fig. 3G., the principal points are 

 A, B, B', B", and the subordinate points, X, C, C', C". 



Enlarge now, 



1. all the faces contiguous to the principal points, till those con- 



tiguous to the subordinate points disappear ; or, 



2. the alternating faces from the principal points, and those from 



