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  • Strategy

Shapes cover curved surfaces efficiently: tortoise


Tortoise bed of rocks / Dan Lieberma.. / LicenseCopyright - All Rights Reserved

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

"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)
About the inspiring organism

Learn more at
Organism/taxonomy data provided by:
Species 2000 & ITIS Catalogue of Life: 2008 Annual Checklist

Bioinspired products and application ideas

Application Ideas: Designs for buildings, packaging, and nanoscale products that utilize 120° angles and filler shapes to create curved shapes and minimize material use.

Industrial Sector(s) interested in this strategy: Architecture, packaging, nanotechnology

Foy S; Oxford Scientific Films. 1982. The Grand Design: Form and Colour in Animals. Lingfield, Surrey, U.K.: BLA Publishing Limited for J.M.Dent & Sons Ltd, Aldine House, London. 238 p.
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