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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. [26] There are 257 topologically distinct convex octahedra, excluding mirror images. More specifically there are 2, 11 ...
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.
Replacing each contact point between two spheres with an edge connecting the centers of the touching spheres produces tetrahedrons and octahedrons of equal edge lengths. The FCC arrangement produces the tetrahedral-octahedral honeycomb. The HCP arrangement produces the gyrated tetrahedral-octahedral honeycomb.
Ørsted experiment (1820): Hans Christian Ørsted demonstrates the connection of electricity and magnetism by experiments involving a compass and electric circuits. Discovery of electromagnetic induction (1831): Michael Faraday discovers magnetic induction in an experiment with a closed ring of soft iron, with two windings of wire.
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:
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagons and 6 squares), 36 edges, and 24 vertices.
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.
Ball-and-stick model of the octadecahedral closo-undecaborate ion, [B 11 H 11] 2−, as found in the crystal structure of the benzyltriethylammonium salt. [1]In geometry, an octadecahedron (or octakaidecahedron) is a polyhedron with 18 faces.
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