论文标题
对Ziegler的猜想进行了反例
Counterexample to a conjecture of Ziegler concerning a simple polytope and its dual
论文作者
论文摘要
问题4.19在Ziegler的“ polytopes上的演讲”中断言，每个简单的$ 3 $尺寸多层都具有其双重属性，即可以将其构造为原始简单多层人物的角度子集的凸面。在本说明中，我们陈述了该猜想的更高维度类似物，并为维度$ d \ geq 3 $提供了一个反例。
Problem 4.19 in Ziegler's "Lectures on Polytopes" asserts that every simple $3$-dimensional polytope has the property that its dual can be constructed as the convex hull of a subset of the vertices of the original simple polytope. In this note we state a higher-dimensional analogue of this conjecture and provide a family of counterexamples for dimension $d \geq 3$.
