50 TERMINOLOGY. . 58. 59. 



. 58. THE HEXAHEDRON. 



The Hexahedron, Fig. 1., is contained under six 

 squares. 



1. All the angles of the hexahedron, those of the faces 

 as well as those of the edges, are = 90. 



2. The sections are rhombohedral, pyramidal, and pris- 

 matic : so are the axes. 



3. The rhombohedral axes pass through the solid angles ; 

 the pyramidal axes, whose number is three, through the 

 centres of parallel faces, and these are perpendicular to each 

 Other ; and this again is general to the pyramidal axes, whenever 

 more than one occur in the same form. The prismatic axes, 

 whose number is six, pass through the centres of parallel 

 edges ; those which belong to parallel edges, intersect each 

 other at right angles ; those which belong to edges that are 

 not parallel, at angles of 60 and 120 ; and tJwse are again 

 general angles for the prismatic axes. 



4. The hexahedron or cube is a regular solid of geometry. 



5. This form is frequently met with in nature, as in 

 octahedral Fluor-haloide, hexahedral Iron-pyrites, &c. 



. 59. THE OCTAHEDRON. 



The Octahedron, Fig. 2., is contained under 

 eight equilateral triangles. 



1. The plane angles of the octahedron are = 60 ; the 

 edges or angles of incidence = 109 28' 16". The angles 

 of incidence of the octahedron and of the tetrahedron are 

 supplemental to each other (to 180). These angles are 

 the same as those at which the rhombohedral axes inter- 

 sect each other (. 57. 3.> 



2. The sections and axes are the same as in the hexahe- 

 dron ; only the rhombohedral axes pass through the centres 

 of parallel faces, and the pyramidal axes through the solid 

 angles. 



