Magnesium 7: the geometry around each atom

What is the geometric arrangement around each magnesium atom? Since it has 12 nearest neighbours, each magnesium atom can be considered to be at the centre of a polyhedron of magnesium atoms with 12 vertices. It is quite a symmetrical object, but not as symmetrical as the cuboctahedron that we saw in the copper structure. It is known as an anticuboctahedron as the triangle that is closest to you when you open the page is twisted 180 degrees relative to its position in the cuboctahedron. It is shown on the left with a green central magnesium atom surrounded by 12 magnesium neighbours in contact, in the shape of an anticuboctahedron.

There are some interesting differences between the anticuboctahedron and the cuboctahedron. The cuboctahedron is more symmetrical because there is only one type of triangular face in it whereas there are two types in the anticuboctahedron - the first type, of which there are two, has edges that adjoin only squares; the second type, of which there are six, has an edge that is shared with another triangle. In effect this property fixes an axis as unique - the axis that passes through the centre of the two triangles of the first type. The cuboctahedron has no unique axis - another indication that it is more symmetrical than the anticuboctahedron. Unlike the cuboctahedron, the anticuboctahedron is not an Archimedean solid: its vertices are not all equivalent. There are two types of vertex: those on the first type of triangle, and all the remaining vertices. These correspond to the A and B layers in the AB representation. However, an equivalent anticuboctahedron can be seen around atoms in the B layer, which goes to show that the two types of layer are still equivalent.

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