is CRYSTALLOGRAPIY. : 
& 
clges, six in number (because the nfiimber of edges is twelve), 
and called the dudecahedral axes. 
Fig. 2 represents the octahedron, a solid contained under 
eight equal triangular faces (whence the name from the Greek 
eight and face), and having the three axes like those in the cube. 
Its plane angles are 60°; its interfacial angles, that is the incli- 
nation of planes 1 and 1 over an intervening edge, 109° 28’; 
and.1 on 1 over a solid angle, 70° 32’. 
Fig. 3 is the dodecahedron, a solid contained under twelve 
equal rhombic faces (whence the name from the Greek for twelve 
and face). The position of the cubic axes is shown in the fig- 
ure. It has fourteen solid angles; six formed by the meeting of’ 
four planes, and eight formed by the meeting of three. The 
interfacial angles (or 2 on an adjoining 7) are 120°: ; 7 on @ over 
a four-faced solid angle =90°. 
Fig. 4isa trapezohedron, a solid contained under 24 equal 
trapezoidal faces. There are several different trapezohedrons 
among isometric crystalline forms. The one here figured, which 
is the common one, ey the angle over the edge B, 131° 49’, 
and that over the edge C, 146° ek trapezohedron 1s ac 
called a tetragonal Papo the faces being tetragonal 
or four-sided, and the number of faces being 3 times 8 (éres, 
octo, in Greek). 
Fig. 5 is another trisoctahedron, one having trigonal or three- 
sided faces, and hence called a trigonal trisoctahedron. Com- 
paring it with the octahedron, fig. 2, it will be seen that three 
of its planes correspond to one of the octahedron. The same is 
true also of the trapezohedron. 
Fig. % isa tetrahexahedron, that is a 4x 6-faced solid, the 
faces being 24 in number, and four corresponding to each face 
of the cube or hexahedron (fig. 1). 
Fig. 7 is a hexoctahedron, that 1s a 6 x 8-faced solid, a pyramid 
of six planes corresponding to eath face in the octahedron, as is 
apparent on comparison. ‘There are different kinds of hexocta- 
hedrons known among crystallized isometric species, as well as 
of the two preceding forms. In each case the difference is not 
in number or general arrangement of planes, but in tre angles 
between the planes, as explained beyond. 
But these simple forms very commonly occur in combination 
with one another ; a cube with the planes of an octahedron and 
the reverse, or with the planes of any or all of the other kinds 
above figured, and many others besides. Moreover, all stages 
between the difierent forms are often represented among the 
crystals of a species. Thus between the cube and octahedron, 
