Flexible Crystal Frameworks
نویسندگان
چکیده
Building upon and complementing recent results on the rigidity theory of periodic bar-and-joint frameworks, this paper studies tetrahedral structures modeled on specific crystalline materials: quartz, cristobalite and tridymite. The general theory predicts at least three infinitesimal degrees-of-freedom. Here, we investigate the actual deformations of these structures. We show that quartz and cristobalite have smooth three-dimensional configuration spaces, but ideal high tridymite is a singular configuration with a six-dimensional tangent space. The topology around this singularity is explicitly described.
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