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What is an octahedron?

What is an octahedron? Here are some definitions.

Noun
  1. (geometry) a polyhedron with eight faces; the regular octahedron has regular triangles as faces and is one of the Platonic solids.
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Finally, the octahedron inscribed in the Venus-orbit sphere has itself an inscribed sphere, on which the orbit of Mercury lies.
While writing, I may choose a clear Quartz Crystal for clarity or a yellow Fluorite octahedron to help keep creative thoughts flowing.
Theaetetus was the first to study the octahedron and the icosahedron and it is believed that Book XIII of Euclid's Elements is based on his work.
These give the solid angles of the tetrahedron, the octahedron and the icosahedron.
This six-point perspective, with the six vertices of an octahedron serving as the vanishing points, becomes the basis of his spherical paintings.
The large four-sided facets above and below and to the right and left of the table are the faces of the octahedron.

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