Every polygon $P$ can be companioned by a cap polygon $\hat P$ such that $P$ and $\hat P$ serve as two parts of the boundary surface of a polyhedron $V$. Pairs of vertices on $P$ and $\hat P$ are identified successively to become vertices of $V$. In this paper, we study the cap construction that asserts equal angular defects at these pairings. We exhibit a linear relation that arises from the cap construction algorithm, which in turn demonstrates an abundance of polygons that satisfy the closed cap condition, that is, those that can successfully undergo the cap construction process.
翻译:每个多边形$P美元都可以与一个上限多边形$$67P美元相伴,例如美元和美元P美元作为多元面的边界表面的两部分。 连续地发现,每个多边形的脊椎是P美元和美元美元,而美元和美元P美元是圆顶的。 在本文中,我们研究了声称这些配对中具有等形缺陷的盖盖结构。 我们展示了从盖盖建筑算法中产生的线性关系,这反过来表明,有大量多边形符合封闭式封顶条件,即那些能够成功进行封顶建造过程的。