Copper 5: the geometry around each copper atom

What is the geometric arrangement around each copper atom? Since it has 12 nearest neighbours, each copper atom can be considered to be at the centre of a polyhedron of copper atoms with 12 vertices. It is evidently a very symmetrical object. That object is actually a cuboctahedron. It is shown on the left with a green central copper atom surrounded by 12 copper neighbours in contact, in the shape of a cuboctahedron.

A cuboctahedron is an Archimedean solid, which means that it has two types of polygon as faces, but that all the vertices are equivalent. ie All 12 copper atom positions are symmetrically equivalent. A buckyball is another example of an Archimedean solid. A cuboctahedron can be made from a cube by slicing off the eight corners all the way down until the faces created at adjacent corners touch at the half way point along the edge of the original cube. The cuboctahedron has six square faces (the remains of the six original cube faces, if you consider it being made by truncating a cube) and eight triangular faces (cut from the eight corners of the cube, if you consider it a truncated cube). The cuboctahedron can also be considered as a truncated octahedron where the corners are simialarly sliced of until the emerging faces meet at the half way point along the edge of the original octahedron. The six corners of the octahedron yield the six square faces of the cuboctahedron upon truncation, and the eight triangles of the cuboctahedron are what remain of the eight faces of the octahedron that is truncated.

Page 6 shows how the cuboctahedron structure is related to the unit cell.

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