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An octahedron can be any polyhedron with eight faces. In a previous example, the regular octahedron has 6 vertices and 12 edges, the minimum for an octahedron; irregular octahedra may have as many as 12 vertices and 18 edges. [24] There are 257 topologically distinct convex octahedra, excluding mirror images. More specifically there are 2, 11 ...
The metal atoms define the vertices of an octahedron. The overall point group symmetry is O h. Each face of the octahedron is capped with a chalcohalide and eight such atoms are at the corners of a cube. For this reason this geometry is called a face capped octahedral cluster. Examples of this type of clusters are the Re 6 S 8 Cl 6 4− anion.
For the cube the extended ƒ-vector is (1,8,12,6,1) and for the octahedron it is (1,6,12,8,1). Although the vectors for these example polyhedra are unimodal (the coefficients, taken in left to right order, increase to a maximum and then decrease), there are higher-dimensional polytopes for which this is not true. [3]
Common net for both a octahedron and a Tritetrahedron.. In geometry, a common net is a net that can be folded onto several polyhedra.To be a valid common net, there shouldn't exist any non-overlapping sides and the resulting polyhedra must be connected through faces.
A regular octahedron can be circumscribed around a cube in such a way that the eight edges of two opposite squares of the cube lie on the eight faces of the octahedron. The three octahedra formed in this way from the three pairs of opposite cube squares form the compound of three octahedra. [1]
The octahedron has eight faces, hence the prefix octa. The octahedron is one of the Platonic solids, although octahedral molecules typically have an atom in their centre and no bonds between the ligand atoms. A perfect octahedron belongs to the point group O h. Examples of octahedral compounds are sulfur hexafluoride SF 6 and molybdenum ...
Example: [11] B 5 H 4− 5. Electron count: 5 × B + 5 × H + 4 (for the negative charge) = 5 × 3 + 5 × 1 + 4 = 24 Since n = 5, 4n + 4 = 24, so the cluster is nido. Starting from an octahedron, one of the vertices is removed. The rules are useful in also predicting the structure of carboranes. Example: C 2 B 7 H 13
It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron . The cube is the three-dimensional hypercube , a family of polytopes also including the two-dimensional square and four-dimensional tesseract .