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What Is a Tetrahedral?

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  • Written By: M.J. Casey
  • Edited By: Daniel Lindley
  • Last Modified Date: 26 November 2016
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Tetrahedral is an adjective that refers to an object that has the geometric shape of a tetrahedron. A tetrahedron is a three-dimensional shape with four triangular faces. Tetrahedral geometries are common in carbon bonds and other chemical bonds. The regular tetrahedron, in which all four faces are identical, has several unique features.

The tetrahedron is also called a triangular pyramid, as pyramids have a four-sided base, usually a square. Four faces form the surface area of a solid tetrahedron. Three edges meet at each vertex or point. The shape has six edges and four vertices. None of the faces is parallel to another. All six edges are of equal length in a regular tetrahedron.

The tetrahedral shape may be short with a wide base, or tall and narrow. The shape is very stable in its shorter or regular configurations. Even tall tetrahedrons are stable if only downward pressure is exerted.

Jack stands for raising car bodies are often tetrahedrons. The three base vertices will not rock, and the vertical force downward spreads equally along the three legs. The legs of a tripod for holding artwork, a camera, or lights form a tetrahedron. A cone, with a circle as the base, is almost as stable if the base rests on a flat surface. The Gateway Arch in St. Louis, Missouri, is the extruded shape of a slowly rotating and arching tetrahedron.

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Essentially, all saturated compounds of carbon, meaning those compounds that do not involve a double or triple bond, are tetrahedral in shape. The methane molecule, CH4, the simplest of these compounds, is a perfect tetrahedron, with a carbon atom in the center and a hydrogen atom at each vertex. Many compounds of silicon, germanium, and tin assume tetrahedral shapes.

Chemical compounds favor the tetrahedral shape because the atoms bound to the central atom are widely dispersed in space. Since they are of the same or similar polarity, the outer atoms will repel each other. The bond angles are 109.5 degrees in methane, the greatest degree of separation possible for an atom with four bonds. For three atoms, the greatest bond angle is 120 degrees, not that much greater than that for four atoms.

Tetrahedral shapes pack well and can completely fill a cubic space if every other layer is inverted. Spheres of equal radii, packed as densely as possible, create cavities between spheres that are regular tetrahedrons. These types of observations are important in crystallography and in elucidating the structure of regularly repeating solids.

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