. 77. OF SIMPLE FORMS IN PARTICULAR. C3 



a. b. c. d. 



1. 77 26' 40". 126 18' 53". 116 6' 13". 93 49' 21". 

 & 80 24' 22". 132 54' 46". 113 21' 46". 113 43' 28". 

 3 82 14' 1". 115 18' 18". 113 34' 41". 123 12' 38*. 



e. A. B. C. 



1. 126 18' 53". 130 W 19". 141 47' 12". 141 47' 12". 



2. 99 35' 38". 135 35' 43". 131 4' 57". 145 57' 8", 



3. 105 40' 22". 149 37' 57". 131 48' 37". 135 35' 43". 



5. This form has not yet been found in nature ; the 

 angles of the three varieties depend upon those of the te- 

 traconta-octahedrons, . 77- 130. 



. 77. TETRACONTA-OCTAHEDR03JS. 



The Tetraconta-octahedrons, Fig. 35., are con- 

 tained under forty-eight scalene triangles. 



1. The solid angles of these forms are bounded by four, 

 six, or eight faces ; they are equiangular and digrammic. 

 Twelve consist of four faces, and are situated above the 

 centres of the faces of the dodecahedron ; eight consist of 

 six faces, and correspond to the solid angles ef the hexahe- 

 dron ; and the remaining six, which consist of eight faces, 

 are distributed like the solid angles of the octahedron. 



2. Of the three different kinds of edges of these forms, 

 the first, being the longest, join the solid angles of six faces 

 with those of eight faces ; the second or intermediate join 

 the solid angles of eight faces with those of four faces ; and 

 the third, which are the shortest, unite the solid angles of 

 six faces with those of four faces. 



3. The sections and axes are as in the hexahedron, In the 

 octahedron, &c. The rhombohedral axes pass through the 

 solid angles of six faces, the pyramidal axes through the 

 solid angles of eight faces, and the prismatic axes through 

 the solid angles of four faces. 



4. There are three varieties of these forms, of the fol- 

 lowing dimensions ; 



