STACHEL HellmuthFlexible cross-polytopes with two flat poses in Euclidean 4-spaceIn 1897, Raoul Bricard proved that there exist three types of flexible octahedra, i.e., polyhedra of the combinatorial type of a regular octahedron with rigid faces and hinges as edges while disregarding self-intersections. Bricard´s type-3 octahedra are unsymmetric and admit two flat poses. Cross-polytopes are the n-dimensional generalizations of octahedra. In 2014, the young Russian mathematician Alexander A. Gaui fullin determined all flexible cross-polytopes in the n-dimensional Euclidean, hyperbolic and spherical spaces for $n>3$. He used algebraic methods. The goal of this presentation is a geometric approach to the geometry of the 4D analogues of type-3 octahedra. They admit two 3-dimensional ´flat´ poses. |