About our logo: The stellated dodecahedron
by John J. Gaines
The stellated dodecahedron ("stellated" comes from Latin stellatus "covered with stars," the past participle of stellare "to set with stars," and "dodecahedron" comes from Greek dodeka "twelve" (see dodeca-) + hedra "face of a geometric solid") is a fascinating geometric shape that has captured the attention of mathematicians, artists, and philosophers throughout history. It is a polyhedron formed by extending the faces of a regular dodecahedron, creating new triangular faces and sharp points. This unique shape has a rich history that spans several centuries, marked by its significance in various fields of study and its aesthetic appeal.
The origins of the stellated dodecahedron can be traced back to ancient Greece, where the study of geometry flourished. The Greek mathematician and philosopher Plato is often credited with the discovery and exploration of regular polyhedra, including the dodecahedron. Plato considered the dodecahedron to be a fundamental element of the universe, associating it with the concept of the fifth element or quintessence, which he believed composed the heavenly bodies. |
Source: Chambers, W., & Chambers, R. (1881). A Dictionary of Universal Knowledge for the People. Philadelphia, PA: J. B. Lippincott & Co.
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While Plato focused on the regular dodecahedron, later mathematicians began investigating its stellations. The process of stellation involves extending the faces of a polyhedron until they intersect to form new faces. Although the concept of stellation was not explicitly described in ancient Greek texts, it gained attention during the Renaissance, particularly through the works of the German astronomer Johannes Kepler.
Source: Kepler, J. (1619) Harmonices Mundi [Harmony of the Worlds]
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Kepler, in his quest to understand the harmony of the universe, explored the stellations of the regular polyhedra, including the dodecahedron. In his book "Harmonices Mundi" (The Harmony of the World), published in 1619, Kepler described the stellated dodecahedron as a celestial shape embodying the harmony of the cosmos. He associated the stellated dodecahedron with the orbit of the planet Mars, believing that the shape represented the planet's trajectory around the Sun.
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The stellated dodecahedron continued to captivate mathematicians and artists in the centuries that followed. In the 19th century, the Belgian artist and mathematician Jean-Charles de Borda introduced the term "stellated" to describe the process of extending the faces of a polyhedron. His work influenced further exploration of stellations and their properties.
One of the most famous depictions of the stellated dodecahedron is found in the works of Dutch artist M.C. Escher. Escher's intricate and mind-bending prints often featured tessellations and complex geometric shapes, including the stellated dodecahedron. His artworks brought the beauty of mathematical concepts to a wider audience, popularizing the stellated dodecahedron as an object of artistic fascination.
Beyond its aesthetic allure, the stellated dodecahedron also holds significance in modern mathematics and computational modeling. It serves as an example of a non-convex polyhedron and has applications in various fields, such as crystallography, computer graphics, and even nanotechnology. Today, the stellated dodecahedron continues to inspire mathematicians, artists, and scientists alike. Its intricate structure, harmonious proportions, and historical significance make it a symbol of the intersection between mathematics, art, and philosophy. Whether admired for its aesthetic appeal or studied for its mathematical properties, the stellated dodecahedron remains a timeless emblem of beauty and intellectual curiosity. |
Source: Escher, M.C. (1948) Stars.
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