Whitney forms are widely known as finite elements for differential forms. Whitney’s original definition yields first order functions on simplicial complexes, and a lot of research has been devoted to extending the definition to nonsimplicial cells and higher order functions. As a result, the term Whitney forms has become somewhat ambiguous in the literature. Our aim here is to clarify the concept of Whitney forms and explicitly explain their key properties. We discuss Whitney’s initial definition with more depth than usually, giving three equivalent ways to define Whitney forms. We give a comprehensive exposition of their main properties, including the proofs. Understanding of these properties is important as they can be taken as a guideline on how to extend Whitney forms to nonsimplicial cells or higher order functions. We discuss several generalisations of Whitney forms and check which of the properties can be preserved.

惠特尼形式被广泛称为微分形式的有限元。惠特尼（Whitney）的原始定义在单纯复形上产生一阶函数，并且许多研究致力于将定义扩展到非单纯性单元和高阶函数。结果，惠特尼形式一词在文学中变得有些模棱两可。我们的目的是澄清惠特尼形式的概念并明确解释其关键特性。我们比通常更深入地讨论惠特尼的初始定义，并给出了三​​种等效的方式来定义惠特尼形式。我们对它们的主要特性（包括证明）进行了全面的阐述。了解这些属性很重要，因为它们可以作为如何将Whitney形式扩展到非简单单元或高阶函数的指南。