# cuboctahedron

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## cuboctahedron

[‚kyü¦bäk·tə′hē·drən]
(mathematics)
A polyhedron whose faces consist of six equal squares and eight equal equilateral triangles, and which can be formed by cutting the corners off a cube; it is one of the 13 Archimedean solids. Also spelled cubooctahedron.
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Buckminster Fuller realized the fundamental nature of the Vector Equilibrium (VE), a geometric structure, also called cuboctahedron.
The elementary neighbourhood on such grids is defined as a cuboctahedron (each pixel having twelve nearest neighbours) which is a shape closer to the sphere than the cube.
The sperrylite crystal is euhedral, without any point of attachment, and is cuboctahedral in habit with rounded edges that give curved outlines to the cuboctahedron faces, similar to the manner in which diamond crystals tend to be rounded.
Joseph DeVincentis suggested the cuboctahedron as a likely shape to use for solid forms--it offers a nice packing of reasonably long words.
A triangular cupola is obtained from a cuboctahedron (Fig 18) cut by a plane containing six edges forming a hexagon (plane ABC on Fig.
At this point, they switched to the PASE module and read about the cuboctahedron.
Crystals could also be combinations of two or more of these forms; for example, a cuboctahedron has eight octahedral faces and another six belonging to a cube (as depicted on page 62).
By using a sequence of elementary moves (moving a vertex along an edge), Morin transforms the cuboctahedron into a curiously shaped figure, which he calls the "central model," with only 12 faces but the same number of vertices as before.
A thumbnail-size pyrite cuboctahedron from Traversella, Piedmont, Italy has, dead in the middle of each octahedron face, a pit of what seems to be pyritohedral outline, all pits being of exactly the same size.
It is a crudely formed cuboctahedron encrusted by a mixture of drusy orthoclase and goethite.
11} and {111} commonly combine to simulate a cuboctahedron.
Other form combinations encountered in the commonly "limonitized" crystals, several centimeters in size, are the cuboctahedron, the cubo-dodecahedron, the pyritohedron/dodecahedron and the pyritohedron/octahedron (Gatel, 1990).

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