hypersurface

The Public Domain Review invites to delve into the fourth dimension with a spectacular gallery of diagrams that anticipate the concept of spacetime and non-Euclidean geometries by British mathematician and science-fiction author Charles Howard Hinton—who first coined the term tesseract (from the Greek τέσσερεις ακτίνες for the four rays that bridge the gap from the edges to the outer vertices) to describe the projection of a cube through a higher facet. As six square faces “net” into a cube, a tesseract—to be depicted in a two dimensional, flat environment—with its twenty-four faces rather defies experience and visualisation and unlike a sphere, cube or pyramid that’s only presented in one way (or perhaps two, rotated—folded or unfolded and face-on), and can be represented in a number of alternate ways (animation helps, and as with any process, some assembly-required) including the iconic cruciform study of Salvador Dalí or the hypercube of La Défense in Paris—a post-modern interpretation of the Arc de Triomphe.