# Tetragonal System and Sphenoidal Class

The Sphenoidal Class corresponds in the Tetragonal System to the Tetrahedral Class in the Isometric System. It is characterized by the following symmetry: The three crystallographic axes are axes of binary symmetry, and there are two vertical diagonal planes of symmetry.

Sphenoid. The characteristic form of the class is known as a sphenoid (from a Greek word meaning alike). It consists of four isosceles triangular faces which intersect all three of the crystallographic axes, the intercepts on the two horizontal axes being equal.

The faces correspond in their position to the alternating faces of the tetragonal pyramid of the first order. There may be different sphenoids, depending upon their varying intersections with the vertical axes. There may also be a positive and a negative sphenoid.

The sphenoid differs from the tetrahedron in the tetrahedron in the fact that its vertical crystallographic axis is not of the same length as the horizontal axes. The only common sphenoidal mineral is chalcopyrite. The length of the vertical axis in chalcopyrite is very close to that of the horizontal axes, c = 0.985. In the case of the unit sphenoid, therefore, it would require accurate measurements in order to differentiate it from an isometric tetrahedron. Chalcopyrite crystals ordinarily show only the unit sphenoid, but at times show a steeper sphenoid.

**Tri – Pyramidal Class**Another division of lower symmetry of the Tetragonal System is known as the Tri-pyramidal Class. It is characterized by a form known as the pyramid of the third order. This form consists of eight faces which correspond in their
position to one-half of the faces of a ditetragonal pyramid. The minerals found in this class are few and rare. Moreover, their crystals seldom sow the faces of the pyramid of the third order, and when these do occur they are usually quite small. Therefore it seems hardily necessary in this place to consider this class in greater detail.

**Characteristic of Tetragonal Crystals**Since the only common tetragonal mineral that does not belong to the Normal class is chalcopyrite, which, moreover, is to be easily recognized by its general physical characterizes, we may confine ourselves here to the consideration only of the crystals of the Normal Class.

The striking characteristics of tetragonal crystals may be summarized as follows: One axis of tetragonal symmetry; the length of the crystal parallel to this axis is usually greater or less than its other dimensions; the cross section of a crystal when viewed in the direction of the axis of tetragonal symmetry consists usually of a square or a truncated square.

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