382 
7. The following are the six systems 
1st. The Cubical ; called also the tesseral, tessular, 
octahedral, regular, isometric, and monometric. 
2nd. The Pyramidal; called also the tetragonal, square 
prismatic, quadratic, monodimetric, dimetric, foui - 
membered, viergliedrig, and the two-and- one axial. 
3rd. The Rhombohedral ; called also the hexagonal, 
monotrimetrical, sechsgliedrig, and the three-and- 
one axial. 
4th. The Prismatic; called also the rhombic, trimetric, 
binary, unisometric, orthotype, orthorhombic, 
zweigliedrig, and one-and-one axial. 
5th. The Oblique; called also the monoclinohedric, 
hemiprismatic, hemiorthotype, clinorhombic, hemi- 
hedric-rhombic, augitic, zwei-und-eingliedng, 
and the two-and- one-membered. 
6th. The Anorthic ; called also the doubly oblique, 
triclinic, triclinohedric, anorthotype, clinorhom- 
boidal, tetarto-prismatic, tetarto-rhombic, einglied- 
ri>, and the one-and-one-membered. 
Cubical System. 
8. The forms of the cubical system possess the highest 
possible degree of symmetry when compared with those of 
the other systems. They are divided into two groups,-— t^e 
holohedral , or perfectly symmetrical, and the hemihedral, or 
half-symmetrical ; the latter being derived from the former 
by being parallel to, or possessing only half their laces, 
grouped together after certain laws. 
9. The holohedral , or perfectly symmetrical forms, are seven 
in number, and are shown on Plate I. Of these, three— the 
cube (fig. 1), the octahedron (fig. 7), and the rhombic 
dodecahedron (fig. 8), are invariable forms, each having but 
one species, and each the same invariable angles, either oi 
their faces or inclination of their faces. 
The remaining four forms are not invariable, and there ai e 
an infinite variety of species, each differing from the other 
in the angles of their faces and their inclinations to each other. 
The half-symmetrical, or hemihedral forms, are represented 
in figs. 15, 17, 19, 21, 23, and 25, Plate III. 
Eolohedral forms, cubical system . 
10. The Cube (fig. 1, Plate I.) is bounded by six equal 
faces, each face, such as 0AO 8 0 4 , being a perfect square; 
