3DPolyfelt was presented at the FAMILY DAY & MATH-ART EXPO, on July 28th, 2013, in Enshede. This is a public activity of the international congress BRIDGES 2013.
(Updated July 30th) We have made the omnitruncation of the fullerene C60! We were glad to see how the ZOME team made the supermolecule C60xC60.
|With Carlo Sequin.|
|With George Hart.|
Recall that the fullerene C60 - the standard buckyball or truncated icosahedron- has 60 vertices, 90 edges, 12 pentagons, and 20 hexagons. The omnitruncation operation consists of cutting the vertices and edges at the same time. The omnitruncation of C60 has then 182 faces: 60 hexagons, 90 squares, 12 decagons, and 20 dodecagons. As each polygon has 10 cm side, the diameter of the balloon which supports the figure will be about 133 cm in diameter. To calculate this diameter we sum the areas of regular polygons 182, equate to the surface of the sphere 4 Pi r ^ 2, and solve for the radius r. Here is the formula programmed in Mathematica L = 10; AreaPoliedron = N[90*4 L^2 /(4 Tan[Pi/4]) + 60*6 L^2 /(4 Tan[Pi/6]) + 12*10 L^2 /(4 Tan[Pi/10]) + 20*12 L^2 /(4 Tan[Pi/12])]; DiameterBalloon = 2 Sqrt[Area/(4 Pi)]).
In our session, our colleague Vi Hart could solve the Menger sponge puzzle in a few minutes! At the end of the video, the artist Rinus Roelofs looks the result.