3D Printed Polyhedron Woodcut by Leonardo da Vinci. Source: Wikipedia Commons
3D Printed Polyhedron Woodcut by Leonardo da Vinci. Source: Wikipedia Commons

In today’s world, we generally think of artists as having an extreme aversion to math (and maybe the other way around too). At first thought the crossover seems pretty minimal, right? But throughout time, there have been talented artists who embrace the other half of their brain and use mathematics to create beautiful images and objects.

The basis of all mathematical forms are geometric shapes called polyhedrons. They all start with the simple 3-dimensional shapes we know and love (pyramid, cube, sphere, etc.) but they get complicated very quickly. Most have tongue-twisting names like “Icosidodecahedron” and “Truncated Rhombic Dodecahedron”. If you speak enough classical Greek, these names describe how many faces the shape has as well as some of its characteristics. If they are lucky, sometimes, these shapes pick up names that are easier to remember (and say). You might know a “regular hexahedron” by its nickname: “cube”.

You might have heard of a man named Leonardo da Vinci. He used polyhedrons in his art somewhat like an athlete uses weights in a gym - they served as challenges to his artistic skills and helped him improve his ability to convey 3-dimensional space on a flat picture plane. Leonardo also saw these shapes as expressions of divine truth because they are an evidence of an ordered universe modeled after the order God set in place as Creator. His beautiful woodcut prints (one pictured here) served as illustrations for his mentors’ book, De Divina Proportione (About Divine Proportions) which was published in 1509.

What is at least as cool as Leonardo’s woodcuts? How about Neolithic stone carved spheres from Scotland? You can clearly see in the photograph that these peoples were exploring mathematical principles in polyhedrons way back then. Look how clearly the incised lines are in these tiny 3 inch spheres. That is some serious stone carving skill!

Hundreds of these carved spheres have been found across Scotland. They were probably created sometime around 2,000 B.C.E. About half have 6 knobs but there are some with as many as 160! Their exact use is unknown. It is also significant that the Dodecahedron (polyhedron with 12 flat faces and one of the primary Platonic solids) appears in this time period, about 1500 years before our first written record of it comes from the Greeks.

One of the great mathematical artists of the 21st Century is George Hart. Mr. Hart is a pioneer in 3D printing. He has seen how it can bring together math and art so easily and effectively. His site is a treasure trove for those who seek to learn more about geometry, 3D printing and their relationship to sculpture. We, at WhiteClouds, use some of Mr. Hart’s designs as inspiration for our own mathematical art. If Leonardo da Vinci was alive, we feel confident that he would be using 3D printing’s capabilities in much the same way as Mr. Hart has done.