Suppose a closed polyhedral surface is built from flat pieces of stiff cardboard taped together along their edges. Will the surface flex? That is; will it change its shape continuously without ripping the tape or bending the cardboard? As an example, let us consider the octahedron shown in Figure 1. If one builds this out of cardboard it turns out to be very rigid and does not flex. However, if the top is slightly smaller than the bottom, the top will pop down as shown in Figure 2. To do this, one must bend the cardboard. Figure 1 will not continuously move into Figure 2 without distortion.
KeywordsPolyhedral Surface Flexible Surface Flat Piece Dimensional Polyhedron Octahedral Framework
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