Socrates (who lives to a hundred) (the 'why' of shapes)
This is Socrates, our school pet. He is a tortoise, which of course means that he has a durably protective exoskeletal shell.
As seen in the picture, the scales (scutes) are hexagons in the centre of the shell, surrounded by slightly irregular pentagons, and then surrounded by a final ring of irregular shapes. The reason for this is that while hexagons tessellate nicely to fill an area, they cannot be bent into the distinct shape of a tortoise’s shell. So the second and third ring of shapes are needed to allow a tension-free dome.
The curved-dome shape of the shell itself also lends to its stability and strength, combined with the material that it is made of. The scutes are made of keratin, the same that human hair and fingernails are made of, that prevent predators from puncturing the shell. But a shell made wholly of keratin brings two issues: weight and cracking. The tortoiseshell solves both these problems by filling the space directly below the outer shell with a sponge-like material that exist in sections separate from the scutes and join together at the edges. This spongy material allows the shell to bend and absorb pressure, while the joints between each section lend the shell a flexibility that prevents the dome from cracking, especially at the centre, where flexibility is minimal compared to other 3D shapes and are therefore prone to cracking.
— Elza Lee (S5)