Nonflexible polyhedra with a small number of vertices
The minimal number of vertices of an embedded or immersed, flexible polyhedral surface in three dimension is still unknown. By considering all combinatorial types of polyhedral surfaces with at most \(8\) vertices, the author shows that this number is either \(7\) or \(8\). It is moreover shown that a flexible polyhedral surface with \(8\) vertices would have to be of one specific combinatorial type. An example with nine vertices was previously known by work of Steffen (1978).
scientific article; zbMATH DE number 5358132