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In geometry, an octahedron (pl.: octahedra or octahedrons) is a polyhedron with eight faces. One special case is the regular octahedron , a Platonic solid composed of eight equilateral triangles , four of which meet at each vertex.
An object with this symmetry is characterized by the part of the object in the fundamental domain, for example the cube is given by z = 1, and the octahedron by x + y + z = 1 (or the corresponding inequalities, to get the solid instead of the surface). ax + by + cz = 1 gives a polyhedron with 48 faces, e.g. the disdyakis dodecahedron.
John Skilling discovered an overlooked degenerate example, by relaxing the condition that only two faces may meet at an edge. This is a degenerate uniform polyhedron rather than a uniform polyhedron, because some pairs of edges coincide. Not included are: The uniform polyhedron compounds.
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. For example, [Co(NH 3) 6] 3+, which is not octahedral in the mathematical sense due to the orientation of the N−H bonds, is referred to as octahedral. [2]
It is the second stellation of the icosahedron, and given as Wenninger model index 23.. It can be constructed by a rhombic triacontahedron with rhombic-based pyramids added to all the faces, as shown by the five colored model image.
If two regular tetrahedra are given the same orientation on the 3-fold axis, a different compound is made, with D 3h, [3,2] symmetry, order 12.. Other orientations can be chosen as 2 tetrahedra within the compound of five tetrahedra and compound of ten tetrahedra the latter of which can be seen as a hexagrammic pyramid:
Dettmore, for example, was very focused on the user experience of a design, so he came up with ways to make certain things more functional in each space, they said.
It can be seen as the compound of an octahedron and a cube.It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot polyhedron and its dual.. It has octahedral symmetry (O h) and shares the same vertices as a rhombic dodecahedron.