20 TERMINOLOGY. 



The Tetrahedron is the most simple of pyramids, having as many 

 bases as it has planes, and on whichever of these it is placed, it is a 

 similarly formed pyramid. It contains the least solidity under a 

 given surface of any natural or artificial solid. It is not a very fre- 

 quent form among crystals, occurring only in Grey Copper Ore, and 

 one or two other mineral species. 



. 35. THE REGULAR OCTAHEDRON.* 



The regular Octahedron is contained under eight equi- 

 lateral triangles. 



* It may not be superfluous to the student, in Mineralogy, who has 

 had little opportunity for the study of solid geometry, to add here a more 

 general description of the properties of the Octahedron. This figure, 

 then, is a solid terminated, or bounded by eight triangular faces, disposed 

 symmetrically about an axis which they meet, four upon one side, and 

 four upon the opposite side, parallel to the first. The Octahedron may 

 be considered as formed by the reunion of two similar and equal four 

 sided pyramids, applied base to base and edge to edge. It will follow, 

 then, that the four edges, ce, ef, fd, dc, Fig. 

 22. of the junction of the two pyramids, are in 

 the same plane, and that they form a parallelo- 

 gram cefd, which is the common base of the 

 pyramids. These edges, ce, ef,fd, dc, are called 

 the edges of the base. The four solid angles c, 

 e, /, and d, are called the angles of the base ; 

 the two remaining solid angles a, and b, the an- 

 gles of the summits, and the line ab, which con- b 

 nects them within, is the axis. The edges which join the angles of the 

 summit with those of the base, are called the upper edges of the Octahe- 

 dron. These are eight in number, and are also, four and four in the same 

 plane, and these two planes, aebd and of be, are also parallelograms. 

 There are, therefore, in an Octahedron, three diagonal planes, or three 

 parallelogramic sections cefd, aebd and of be. It is obvious that any one 

 of these may be chosen for the base of an Octahedron, which being- 

 selected, the line which joins the two opposite angles, not comprised in 

 the adopted base, will be the vertical axis. There are, then, three 

 bases, and three axes in this solid ; but in the crystals which come under 



