Buckyball, Truncated Icosahedron, Soccer Ball, C60

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Multiple Ways to Have Fun with the Buckyball, Truncated Icosahedron, Soccer Ball, C60, Halves In honor of Prof. Buckminster Fuller, who inspired countless minds at SIU Carbondale in the 1960s. The buckyball is an awe-inspiring structure! It's a harmonious arrangement of 20 regular hexagons and 12 regular pentagons that showcases incredible mathematical properties. In the world of 3D design, we can create a buckyball from an icosahedron by leveraging its unique features. To get started, make an icosahedron (one of the five Platonic solids) using a regular triangle and extrusion techniques or other methods. A basic understanding of dihedral angles is essential for this process. Next, slice off all 12 vertices of the icosahedron using a plane that passes through one-third of its edge length around each vertex. If the original icosahedron has an edge length of 30 mm, the resulting buckyball will have an edge length of 10 mm. Each vertex of the icosahedron collapses into a pentagon, while each regular triangle transforms into a regular hexagon. This transformation creates a stunning and symmetrical structure that's both mathematically appealing and visually captivating. Among the Files 1. The measurements provided refer to the original edge length of the foundational icosahedron. 2. Solid buckyballs come in various sizes, each with its unique characteristics. 3. Shelled buckyballs offer a range of styles and sizes, allowing for creative experimentation. 4. Wired buckyballs provide an added level of complexity and visual interest. 5. Half buckyballs (with hexagonal and pentagonal bottoms) cannot be mixed, but combining two identical halves creates a complete buckyball. References 1. https://ethw.org/Discovering_the_Buckyball 2. https://en.wikipedia.org/wiki/Buckminsterfullerene 3. https://www.popsci.com/buckyball-magic-molecule 4. https://eic.rsc.org/feature/symmetry-of-buckminsterfullerene/2020237.article 5. https://www.forbes.com/sites/kevinknudson/2015/07/23/the-mathematics-of-buckyballs/#1b346d946f77 6. https://en.wikipedia.org/wiki/Buckminster_Fuller 7. Curl, Robert F., and Richard E. Smalley. "Fullerenes." Scientific American 265, no. 4 (1991): 54-63. http://www.jstor.org/stable/24938758.