论文标题
四角凸金字塔的几何形状
The geometry of quadrangular convex pyramids
论文作者
论文摘要
如果它属于\ emph {abcd $ abcd $，$ abcd $是基础，而顶点则称为\ emph {abcd $，则称为\ emph {强弹性}，如果它属于一个持续的成对非兼容性四边形的四角形金字词，具有相同的相应边缘长度。如果不存在此类家庭，则$ abcde $称为\ emph {强刻。我们证明了凸四角形金字塔的强刚度，并证明了在自我交流的情况下强刚性失败。令$ l = \ {l_1，\ ldots，l_8 \} $是一组正数，那么$ l $的a \ emph {实现}是一个convex quadrangular pyramid $ abcde $，例如$ | ea | = l_5 $，$ | eb | = l_6 $，$ | ec | = l_7 $，$ | ed | = l_8 $。我们证明，成对的非统一实现的数量为$ \ leqslant 4 $，并给出了一个套装$ l $的示例，并带有三个成对的非统一实现。
A convex quadrangular pyramid $ABCDE$, where $ABCD$ is the base and $E$ -- the apex, is called \emph{strongly flexible}, if it belongs to a continuous family of pairwise non-congruent quadrangular pyramids that have the same lengths of corresponding edges. $ABCDE$ is called \emph{strongly rigid}, if such family does not exist. We prove the strong rigidity of convex quadrangular pyramids and prove that strong rigidity fails in the self-intersecting case. Let $L=\{l_1,\ldots,l_8\}$ be a set of positive numbers, then a \emph{realization} of $L$ is a convex quadrangular pyramid $ABCDE$ such, that $|AB|=l_1$, $|BC|=l_2$, $|CD|=l_3$, $|DA|=l_4$, $|EA|=l_5$, $|EB|=l_6$, $|EC|=l_7$, $|ED|=l_8$. We prove that the number of pairwise non-congruent realizations is $\leqslant 4$ and give an example of a set $L$ with three pairwise non-congruent realizations.
