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A regular octahedron is an octahedron that is a regular polyhedron. All the faces of a regular octahedron are equilateral triangles of the same size, and exactly four triangles meet at each vertex. A regular octahedron is convex, meaning that for any two points within it, the line segment connecting them lies entirely within it.
Tridentate ligands usually bind via two kinds of connectivity, called "mer" and "fac." "fac" stands for facial, the donor atoms are arranged on a triangle around one face of the octahedron. "mer" stands for meridian, where the donor atoms are stretched out around one half of the octahedron.
A perfect octahedron belongs to the point group O h. Examples of octahedral compounds are sulfur hexafluoride SF 6 and molybdenum hexacarbonyl Mo(CO) 6 . The term "octahedral" is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves.
If the three donor atoms are arranged on a meridian, β-mer- is used; if the three donor atoms are arranged on the face of an octahedron, β-fac is used. [1] The chain can have two bends, with one donor at a pole, two on the equator and one at the opposite pole. None of the triangles of coordinating atoms and the central atom are coplanar.
A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has the same set of symmetries, since it is the polyhedron that is dual to an octahedron.
In geometry, the elongated square bipyramid (or elongated octahedron) is the polyhedron constructed by attaching two equilateral square pyramids onto a cube's faces that are opposite each other. It can also be seen as 4 lunes (squares with triangles on opposite sides) linked together with squares to squares and triangles to triangles.
In another approach known as the horizontal coordinate system, the meridian is divided into the local meridian, the semicircle that contains the observer's zenith and the north and south points of their horizon, [1] [2] and the opposite semicircle, which contains the nadir and the north and south points of their horizon.
In geometry, a Bricard octahedron is a member of a family of flexible polyhedra constructed by Raoul Bricard in 1897. [1] The overall shape of one of these polyhedron may change in a continuous motion, without any changes to the lengths of its edges nor to the shapes of its faces. [ 2 ]