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The Logo of the Division of Mathematical Biology is an icosahedral virus shell formed from plastic monkeys by Michael Green.

Monkeys ape Molecules

Virus coats, muscle fibres, mitotic spindles and many other regular biological structures are assembled from multiple copies of protein molecules, linked together by specific bonds. Protein molecules are inherently asymmetric and it is difficult to represent their interactions using regular shapes (spheres or ellipsoids). The monkey provides a large scale unit, which because of its asymmetry and the many potential links, can simulate the geometrical relationships within complex structures and can illuminate some general principles of symmetry.

Plastic monkeys can be joined in pairs in over eighty different ways (Nature, 219, 413, (1968)). The links between them can be either asymmetric (A) or symmetric (S).Any pair can be used as a nucleus for further growth. If the first link is asymmetric (A), it joins a site X on the first monkey to a site Y on the second and leaves a spare X site on the second monkey and a Y site on the first, which can be used to add further monkeys and so generate a simple helix from a single type of A link. Asymmetric links can also be used to make rings with differing upper and lower surfaces.

If instead of linking X to Y we link X to the X site of another monkey, the monkeys will be joined by a symmetrically and no further growth can occur unless a new kink Z is introduced, which in turn may be either asymmetric or symmetric

A hierarchy of structures generated in this way is shown, to illustrate the versatility of this species of monkey.