论文标题
概括连续柔性的异教体类型的Kokotsakis腰带
Generalizing continuous flexible Kokotsakis belts of the isogonal type
论文作者
论文摘要
Kokotsakis在1932年研究了以下问题：给定的是刚性闭合的多边形线（平面或非平面），该线被多面层带包围，每个Polygon顶点在每个Polygon顶点，三个面相遇。用连续迁移率确定这些封闭条的几何形状。一方面，我们通过允许与多边形线段相邻的面部偏向偏斜来概括这个问题。即非平面。但是另一方面，我们仅限于与每个多边形顶点相关的四个角度满足所谓的同性恋条件的情况，即两对相反角度都相等或补充。更详细地，我们研究了多边形线是偏斜四边形的情况，因为这对应于由偏斜四边形组成的所谓V-Hedra的（3x3）构建块。后者还为罗伯特·索尔（Robert Sauer）在1970年的书中提出的一个问题提供了积极的答案，是否存在连续的柔性四边形表面。
Kokotsakis studied the following problem in 1932: Given is a rigid closed polygonal line (planar or non-planar), which is surrounded by a polyhedral strip, where at each polygon vertex three faces meet. Determine the geometries of these closed strips with a continuous mobility. On the one side, we generalize this problem by allowing the faces, which are adjacent to polygon line-segments, to be skew; i.e to be non-planar. But on the other side, we restrict to the case where the four angles associated with each polygon vertex fulfill the so-called isogonality condition that both pairs of opposite angles are equal or supplementary. In more detail, we study the case where the polygonal line is a skew quad, as this corresponds to a (3x3) building block of a so-called V-hedra composed of skew quads. The latter also gives a positive answer to a question posed by Robert Sauer in his book of 1970 whether continuous flexible skew quad surfaces exist.
