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TETRAHEDRAL

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Originally appearing in Volume V07, Page 576 of the 1911 Encyclopedia Britannica.
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TETRAHEDRAL CLASS (Tetrahedral-hemihedral; Hexakis-tetrahedral). In this class there is no centre of symmetry nor cubic planes of symmetry; the three tetrad axes become dyad axes of symmetry, and the four triad axes are polar, i.e. they are associated with different faces at their two ends. The other elements of symmetry (&x dodecahedral planes and six dyad axes) are the same as in the last class. Of the seven See also:

simple forms, the See also:cube, rhombic See also:dodecahedron and tetrakis-hexahedron are geometrically the same as before, though on actual crystals the faces will have different See also:surface characters: For instance, the cube faces will be striated parallel to only one of the diagonals (fig. 90), and etched figures on this See also:face will be symmetrical with respect to two lines, instead of four as in the last class. The remaining simple forms have, however, only See also:half the number of faces as the corresponding See also:form in the last class, and are spoken of as " hemihedral with inclined faces." See also:Tetrahedron (fig. 26). This is bounded by four equilateral triangles and is identical with the See also:regular tetrahedron of See also:geometry. The angles between the normals to the faces are 109° 28'. It may be derived from the See also:octahedron by suppressing the alternate faces. Deltoid 1 dodecahedron (fig. 27).

This is the hemihedral form of the triakis-octahedron; it has the indices lhhk} and is bounded by twelve trapezoidal faces. l From the See also:

Greek See also:letter SiXra, d; in See also:general, a triangular-shaped See also:object; alsoan alternative name for a trapezoid. Triakis-tetrahedron (fig. 28). The hemihedral form lhkklof the icositetrahedron; it is bounded by twelve isosceles triangles arranged in threes over the tetrahedron faces. Hexakis-tetrahedron (fig. 29). The hemihedral form {hkll of the hexakis-octahedron; it is bounded by twenty-four scalene triangles and is the general form of the class. Tetrahedra. hedron and Cubes Corresponding to each of these hemihedral forms there is another geometrically similar form, differing, however, not only in See also:orientation, but also in actual crystals In the characters of the faces. Thus from the octahedron there may be derived two tetrahedra with the indices {1111 and { Y I I I, which may be distinguished as See also:positive and negative respectively. Fig. 30 shows a See also:combination of Tetrahedron, Cube and Rhombic Tetrahedron and Rhombic Dodecahedron.

Dodecahedron. these two tetrahedra, and represents a crystal of See also:

blende, in which the four larger faces are dull and striated, whilst the four smaller are See also:bright and smooth. See also:Figs. 31-33 illustrate other tetrahedral combinations. See also:Tetrahedrite, blende, See also:diamond, See also:boracite and See also:pharmacosiderite are substances which crystallize in this class. PYRITOHEDRALl CLASS (Parallel-faced hemihedral; Dyakis-dodecahedral). Crystals of this class possess three cubic planes of symmetry but no dodecahedral planes. There are only three dyad axes of symmetry, which coincide with the crystallographic axes; in addition there are three triad axes and a centre of symmetry. Here the cube, octahedron, rhombic dodecahedron, triakis-octahedron and icositetrahedron are geometrically the same as in the first class. The characters of the faces will, however, be different; thus the cube faces will be striated parallel to one edge only (fig. 89), Pentagonal Dodecahedron. Dyakis-dodecahedron.

and triangular markings on the octahedron faces will be placed obliquely to the edges. The remaining simple forms are " hemihedral with parallel faces," and from the corresponding See also:

holohedral forms two hemihedral forms, a positive and a negative, may be derived. Pentagonal dodecahedron (fig. 34). This is bounded by twelve pentagonal faces, but these are not regular pentagons, and the angles over the three sets of different edges are different. The regular dodecahedron of geometry, contained by twelve regular pentagons, is not a possible form in crystals. The indices are lhkol : as a simple form 12I01is of very See also:common occurrence in See also:pyrites. Dyakis-dodecahedron (fig. 35). This is the hemihedral form of l Named after pyrites, which crystallizes in a typical form of this class. c '576 the hexakis-octahedron and has the indices (hkl) ; it is bounded by twenty-four faces. As a simple form 1321) is met with in pyrites.

Combinations (figs. 36-39) of these forms with the cube and the octahedron are common in pyrites. Fig. 37 resembles in general See also:

appearance the regular See also:icosahedron of geometry, but only eight of the faces are equilateral triangles. See also:Cobaltite, See also:smaltite and other sulphides and sulpharsenides of the pyrites See also:group of minerals crystallize in these forms. The alums also belong to this class; from an aqueous See also:solution they crystallize as simple octahedra, PentagonalDodecahedron,Cube Pentagonal Dodecahedron e and Octahedron. 1210 , Dyakisdodecahedron f 1321), and Octahedron d 11111.

End of Article: TETRAHEDRAL

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