A convex polygon $A$ is related to a convex $m$-gon $K= \bigcap_{i=1}^mk_i^+$, where $k_1^+,..., k_m^+$ are the $m$ halfplanes whose intersection isequal to $K$, if $A$ is the intersection of halfplanes $a_1^+,...,a_l$, each ofwhich is a translate of one of the $k_i^+$-s. The planar family ${\cal A}$ isrelated to $K$ if each $A \in {\cal A}$ is related to $K$. We prove that anyfamily of pairwise intersecting convex sets related to a given $n$-gon has afinite piercing number which depends on $n$. In the general case we show$O(3^{n^3})$, while for a certain class of families, we decrease the bound to$4(n-2)$, and for $n=3,4$ the bound is 3 and 6 respectively.
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机译：凸多边形$ A $与凸$ m $ -gon $ K = \ bigcap_ {i = 1} ^ mk_i ^ + $相关，其中$ k_1 ^ +，...，k_m ^ + $是$ m如果$ A $是半平面$ a_1 ^ +，...，a_l $的交点，则其交点等于$ K $的$个半平面，每个半平面都是$ k_i ^ + $-s之一的转换。如果{\ cal A} $中的每个$ A与$ K $相关，则平面族$ {\ cal A} $与$ K $相关。我们证明与给定的$ n $ -gon相关的成对相交凸集的任何族都有一个取决于$ n $的无穷穿孔数。在一般情况下，我们显示$ O（3 ^ {n ^ 3}）$，而对于某些类别的家庭，我们将边界减小到$ 4（n-2）$，而对于$ n = 3.4，$绑定分别是3和6。
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