Ancient Greek mathematicians – most notably Plato – classified solid shapes thousands of years ago.
Since then, remarkably few geometric ‘solid’ forms have been discovered and the last collection was identified 400 years ago.
But now, U.S. scientists believe they have identified a fourth class of shape called a Goldberg polyhedra, which they say is inspired by shapes in the human eye.
The first type of solid shapes to be discovered are known as Platonic solids, which include the cube, the tetrahedron (a 3D form made up of four triangular faces), the octahedron (a 3D form made up of eight triangles), the dodecahedron (a 3D form made up of 12 sides) and the icosahedron (a form made up of 20 triangular faces and 30 edges).
All these shapes are highly regular and occur naturally.
Just two other types of solid shapes have been documented after these: Archimedean solids, which include the truncated icosahedron (a 32-faced solid shape), and incredibly complex 3D forms called Kepler solids, which were discovered 400 years ago and include the rhombic polyhedra.
But now the new type of shape, which looks a little bit like a complex football, has been explained mathematically and could even pave the way for an infinite number of similar shape classes to be discovered, The Conversation explained.
Stan Schein at the University of California in Los Angeles was studying the retina of the human eye when he came across the intriguing polyhedra structure of a protein called clahrin, which moves energy in and out of cells and creates a number of shapes.
He came up with a mathematical explanation for the shape and in the process, stumbled across the work of Michael Goldberg, a 20th century mathematician who was convinced he had discovered a new set of shapes – complicated polyhedra made up of a patchwork of pentagons and hexagons.
While Dr Schein did not think that Goldberg’s shapes were strictly polyhedra, he believed they were indeed a new class of shape.
In a study published in the journal PNAS, Dr Schein and James Gayed describe the new shapes, which they still call the Goldberg polyhedral in tribute to the late mathematician.
Controversially, the original Goldberg polyhedra break the third rule of the classification of equilateral complex polyhedra – that any point on a line that connects two points in a shape must not fall outside the solid shape.
The U.S. mathematicians however carefully manipulated them so that instead of a bulgy shape composed of multiple hexagons, they found a way of making all the faces of the shapes flat so that a true convex polyhedron was created.
They think their way of manipulating the shapes can be applied to other classes of complex polyhedra so that further shapes will be discovered with more and more faces and that in theory there should be an infinite number of them.
While it might be difficult for non-mathematicians to think of immediate uses for this piece of research, it has excited some scientists as the new polyhedra have similar structures to viruses.
If scientists could accurately describe the geometry of a virus, such as common flu, they might be able to find a better way of fighting them.
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