Dodecahedron Buckyball, Holiday Ornaments

thingiverse

The simplest buckyball is a dodecahedron, featuring 12 regular pentagon faces. By extruding each of these pentagons at an optimal angle, allowing all vertices to align on the same sphere (the circumscribing sphere), we create a dodecahedral buckyball. In this design, the circum-radius of the pentagon is 30 mm, its edge length approximately 35.26 mm, and the radius of the dodecahedron's circumsphere about 49.42 mm. The optimal taper angle for extrusion is approximately -67.3 degrees. My calculation: -90 deg + atan((dodecaCircumedSphereRadius - dodecaInscribedSphereRadius) / (tan(54 deg) * edgeLen / 2)). Among the files you'll find: 1. A solid, detailed dodecahedron buckyball. 2. A shelled version with a pentagonal opening at the bottom. 3. A wireframe representation of this unique shape. 4. A shelled dodecahedron design for your exploration.