0.3 Minimum Surfaces

0.3 Minimum Surfaces There is a natural connection between the surfaces delimiting a rhombic dodecahedron and the minimum surfaces determined by the soap films. Next, we will provide the facts that support this assessment, using the same approach used before in these videos. We will let the 3-D views of CPS patterns and structures speak for themselves. Joseph Plateau discovered experimentally, over a hundred years ago, that soap films contained by a framework always satisfy three geometrical conditions: 1. Three smooth surfaces of a soap film intersect along a line; 2. The angle between any two tangent planes to the intersecting surfaces, at any point along the line of intersection of three surfaces is 120 degrees. 3. Four of the lines, each formed by the intersection of three surfaces meet at a point and the angle between any pair of adjacent lines is 109.28 degrees.