. 64. OF SIMPLE FORMS IN PARTICULAR. 53 



1. The plane angles of these rhombs are = 109 28' 16" 

 and 70 31' 44", equal to the edges of the octahedron (. 59. 

 1.) and of the tetrahedron. They are equal also to the 

 angles of intersection of the rhombohedral axes (. 57. 1. 

 3.). The edges are all = 120. 



2. The raonogrammic Tetragonal-dodecahedron has eight 

 solid angles formed by three, and six formed by four faces ; 

 both of them are equiangular. The first are situated like 

 the solid angles of the hexahedron, the second like those of 

 the octahedron. 



3. The sections and axes are as in these. The rhombohe- 

 dral axes pass through the solid angles of three, the pyrami. 

 dal axes through the solid angles of four faces, and the pris- 

 matic axes through the centres of parallel faces of the solid. 



4. There is only one variety of this form, which is com- 

 monly expressed by the name of the Dodecahedron. 



5. The dodecahedron is not a rare form ; it is found in 

 dodecahedral Garnet, hexahedral Gold, &c. 



. 64-. DIGRAMMIC TETRAGONAL-DODECAHEDRONS. 



The faces of the digrammic Tetragonal-dodeca- 

 hedrons, Figs. 17. 18., possess the outlines of those 

 inscribed in a Trapezium. 



1. The digrammic Tetragonal-dodecahedrons have the 

 general aspect of the tetrahedron. 



2. They contain two kinds of solid angles formed by three 

 faces, four of each. Both kinds are equiangular. The 

 more acute correspond to the solid angles, the more obtuse 

 to the centres of the faces of the tetrahedron. They possess 

 moreover six solid angles of four faces, which are equian- 

 gular, but digrammic, and situated above the centres of the 

 edges of the tetrahedron. 



3. Of the two kinds of edges of these forms, the more ob- 

 tuse join in the obtuse, the more acute in the acute solid 

 angles formed by three faces, and both in the solid angles 

 consisting of four faces. 



