The shell of tortoises optimizes material use for a curved surface via hexagonal subunits and filler shapes.

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“Inevitably nature is not always exact, despite the precision of the honeycomb. When looking for 120° angles in animal forms it is important to remember another geometric law, which is that flat hexagons will only interlock in a flat plane; they cannot be combined to enclose a space, as can the triangles that constitute the tetrahedron. Where hexagons do occur on curved surfaces — such as in the beautifully delicate skeletons of some microscopic marine organisms called Radiolaria — there are always some other shapes and angles inserted to compensate for the curvature. The same is true of the tortoise’s shell, where remarkably regular hexagons in the centre are bounded by pentagons (five-sided shapes) which fuse to give a straight edge to the shell; exactly the same happens in insect wings. Three-way junctions also tend to occur where pieces of similar size and shape must be overlapped to cover a surface, as in the feathers of a bird, the scales of a fish, or the scales of a pangolin.” (Foy and Oxford Scientific Films 1982:32)

The grand design: Form and colour in animalsJanuary 17, 1983
Sally Foy

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