Periodic table of shapes to include several dimensions

Mathematicians are creating their own version of the periodic table that will provide a directory of all the possible shapes in the universe across three, four and five dimensions, linking shapes together in the same way as the periodic table links groups of chemical elements.

The three-year project should provide a resource that mathematicians, physicists and other scientists can use for calculations and research in a range of areas, including computer vision, number theory and theoretical physics.

The researchers, from Imperial College London and institutions in Australia, Japan and Russia, are aiming to identify all the shapes across three, four and five dimensions that cannot be divided into other shapes.

Project leader Professor Alessio Corti, from the Department of Mathematics at Imperial College London, explained: "The periodic table is one of the most important tools in chemistry. It lists the atoms from which everything else is made and explains their chemical properties. Our work aims to do the same thing for three-, four- and five-dimensional shapes - to create a directory that lists all the geometric building blocks and breaks down each one’s properties using relatively simple equations. We think we may find vast numbers of these shapes, so you probably won’t be able to stick our table on your wall, but we expect it to be a very useful tool."

The researchers calculate that there are around 500 million shapes that can be defined algebraically in four dimensions and they anticipate that they will find a few thousand building blocks from which all these shapes are made.