Whitney forms and their extensions

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 nonsimplicial cells higher functions. As result, term become somewhat ambiguous in literature. Our aim here is clarify concept explicitly explain their key properties. We discuss initial with more depth than usually, giving three equivalent ways define give comprehensive exposition main properties, including proofs. Understanding these properties important they can be taken guideline how extend or several generalisations check which preserved.