A combinatorial polytope P is said to be projectively unique if it has a single realization up to projective transformations. Projective uniqueness is a geometrically compelling property but is difficult to verify. In this paper, we merge two approaches to projective uniqueness in the literature. One is primarily geometric and is due to McMullen, who showed that certain natural operations on polytopes preserve projective uniqueness. The other is more algebraic and is due to Gouveia, Macchia, Thomas, and Wiebe. They use certain ideals associated to a polytope to verify a property called graphicality that implies projective uniqueness. In this paper, we show that McMullen’s operations preserve not only projective uniqueness but also graphicality. As an application, we show that large families of order polytopes are graphic and thus projectively unique.

组合多胞体P如果它具有直到投影变换的单一实现，则称它是投影唯一的。投影唯一性是几何上引人注目的属性，但很难验证。在本文中，我们合并了文献中两种投影唯一性的方法。一个主要是几何的，这要归功于 McMullen，他表明对多胞体的某些自然运算保留了投影唯一性。另一个是更代数的，是由于 Gouveia、Macchia、Thomas 和 Wiebe。他们使用与多面体相关的某些理想来验证一种称为图形性的属性，该属性意味着投影唯一性。在本文中，我们表明 McMullen 的操作不仅保留了投影唯一性，还保留了图形性。作为一个应用，我们展示了大家族的有序多胞体是图形的，因此在投影上是独一无二的。