. 60. 61. OF SIMPLE FORMS IN PARTICULAR. 51 



3. The octahedron is a regular solid of geometry. 



4. This form occurs very frequently in different species, 

 as in octahedral Corundum, octahedral Iron-ore, &c. 



. 60. DODECAHEDRONS IN GENERAL. 



The Dodecahedrons are contained under twelve 

 equal and similar faces, the figure of which deter-- 

 mines the kind of the dodecahedrons. A dodeca- 

 hedron whose faces are triangles, is termed a 

 Trigonal-dodecahedron ; one whose faces are tetra-* 

 gons, a Tetragonal-dodecahedron ; and one whose 

 faces are pentagons, a Pentagonal-dodecahedron. 



1. None of these dodecahedrons are regular in the geo- 

 metrical sense of the word ; for their faces are not regular 

 polygons ; besides, they have at least two different kinds of 

 angles, and, one of the dodecahedrons only excepted, they 

 have also at least two kinds of edges. 



. 61. TRIGONAL-DODECAHEDRONS. 



The Trigonal-dodecahedrons, Figs. 15. 16., are 

 contained under equal and similar isosceles triangles. 



1. The trigonal-dodecahedrons possess the general aspect 

 of the tetrahedron, and their sections and axes are of the 

 same kind, and in the same situation. 



2. They contain four solid angles of three, and four of 

 six faces ; both of them being equiangukr. The first are 

 monogrammic, and correspond to the centres of the faces ? 

 the others are digrammic, and correspond to the solid angles 

 of the tetrahedron. 



3. Of the two kinds of edges of the trigonal-dodecahe- 

 drons, the first, or those joining the angles of six faces, 

 have the situation of the edges of the tetrahedron ; the 

 others meet in the solid angles of three faces, upon the 

 centre of the faces of that form. 



