. 72. 73. OF SIMPLE FORMS IN PARTICULAR. 59 



. 5. The second variety occurs in dodecahedral Garnet, 

 the third in octahedral Fluor-haloide ; the angles of the 

 first depend upon those of the first variety of the dodeca- 

 hedrons, . 66. 130. 



. 72. OCTAHEPRAL TRIGONAL-ICOSITETRAHEDRONS. 



The faces of the octahedral Trigonal-icositetra- 

 hedrons, Fig. 33., are isosceles triangles. 



1. Their solid angles consist of either three or eight 

 faces, and are equiangular. The first, eight in number, 

 are monogrammic, and correspond to the centres of the 

 faces ; the second, six in number, are digrammic, and cor- 

 respond to the angles of the octahedron. 



2. Those edges, which have the situation of those of the 

 octahedron, join the solid angles of eight faces with each 

 other ; the other edges unite two dissimilar solid angles. 



3. The sections and axes are as in the octahedron. 



4. There is only one variety known, of the following 

 dimensions : 



a. b. A. B. 



118 4' 10". 30 57' 55". 141 3' 28". 152 44' 2". 

 4. Examples of this form are found in octahedral Fluor- 

 haloide, hexahedral Lead^glance, &c. 



. 73. TETRAGONAL-ICOSITETRAHEDRONS. 



The Tetragonal-icositetrahedrons, are contained 

 under equal and similar tetragonal faces. 



1. This species of icositetrahedrons comprises two kinds, 

 the varieties of which are distinguished from each other by 

 the figures of their faces, and by several properties depend- 

 ing upon them, chiefly by the diversity of their edges, ac- 

 cording to which, they also receive their denominations. 



2. The varieties of the first kind, contain only two dif- 

 ferent edges, and are termed digrammic ; whilst the second, 



