A tetrahedron is a three-dimensional shape with four triangular faces, commonly found in carbon and other chemical bonds. It has six edges and four vertices, with all edges of equal length in a regular tetrahedron. The shape is stable and can be short or tall. Chemical compounds favor the tetrahedral shape due to widely dispersed atoms. Tetrahedral shapes pack well and can fill a cubic space.
Tetrahedron 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 quadrilateral base, usually square. Four faces form the surface of a solid tetrahedron. Three edges meet at each vertex or point. The shape has six edges and four vertices. Neither face is parallel to the other. All six edges are of equal length in a regular tetrahedron.
The tetrahedral shape can 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 applied.
Jack’s about to lift the car bodies are often tetrahedrons. The three base vertices will not swing and the downward vertical force 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 a 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 tetrahedron that slowly rotates and arches.
Basically, all carbon-saturated compounds, i.e. 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 at the center and a hydrogen atom at each corner. Many compounds of silicon, germanium and tin take on tetrahedral shapes.
Chemical compounds favor the tetrahedral shape because the atoms bonded to the central atom are widely dispersed in space. Because they are of the same or similar polarity, the outer atoms repel each other. Bond angles are 109.5° in methane, the maximum degree of separation possible for an atom with four bonds. For three atoms, the largest bond angle is 120 degrees, not much greater than for four atoms.
Tetrahedral shapes pack well and can completely fill a cubic space if every other layer is reversed. Spheres of equal radii, packed as densely as possible, create cavities between spheres that are regular tetrahedra. These types of observations are important in crystallography and in elucidating the structure of regularly repeating solids.
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