TETARTOHEDRAL

This article appears in Volume V07, Page 576 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: TAV-THE

TETARTOHEDRAL CLASS
(Tetrahedral pentagonal dodecahedral).
Here, in addition to four polar triad axes, the only other elements of symmetry are three dyad axes, which coincide with the crystallo-
i From a)6ycos, placed sideways, referring to the

absence

ABSENCE (Lat. absentia)

of planes and centre of symmetry.
2 From yipos, a ring or spiral, and tlSos, form.graphic axes. Six of the simple forms, the

cube

CUBE (Gr. K46os, a cube)

, tetrahedron, rhombic

dodecahedron

DODECAHEDRON (Gr. Melia, twelve, and ESpa, a face or base)

, deltoid

dodecahedron

DODECAHEDRON (Gr. Melia, twelve, and ESpa, a face or base)

, triakis-tetrahedron and pentagonal dodecahedron, are geometrically the same in this class as in either the tetrahedral or pyritohedral classes. The general form is the
Tetrahedral pentagonal dodecahedron (fig. 41). This is bounded by twelve irregular pentagons, and is a tetartohedral or

quarter

QUARTER (through Fr. from Lat. quartarius, fourth
part
- PART
)

-faced form of the hexakis-

octahedron

OCTAHEDRON (Gr. 6K-rw, eight, Mpa, base)

. Four such forms may be derived, the indices of which are {hkl), {khll, 1hkl) and (khl); the first pair are enantiomorphous with respect to one another, and so are the last pair. Barium nitrate, lead nitrate, sodium chlorate and sodium bromate crystallize in this class, as also do the minerals ullmannite (NiSbS) and langbeinite (K2Mg2(SO4)2).
2. TETRAGONAL SYSTEl1
(Pyramidal; Quadratic; Dimetric).
In this

system

SYSTEM

the three crystallographic axes are all at right angles, but while two are equal in length and interchangeable the third is of a different length. The unequal

axis

AXIS (Lat. for " axle ")

is spoken of as the

principal

PRINCIPAL

axis

AXIS (Lat. for " axle ")

or morphological axis
of the crystal, and it is always placed in a vertical position ; in five of the seven classes of this

system

SYSTEM

it coincides with the single tetrad axis of symmetry.
The parameters are a: a: c, where a refers to the two equal hori-
zontal axes, and c to the vertical axis; c may be either shorter (as in fig. 42) or longer (fig. 43) than a. The ratio a: c is spoken of as the axial ratio of a crystal, and it is dependent on the angles between the faces. In all crystals of the same substance this ratio is constant, and is characteristic of the substance; for other substances crystallizing in the tetragonal system it will be different. For example, in cassiterite it is given as a : c =I: 0.67232 or simply as c =0.67232, a being unity; and in anatase as c =1.7771.

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