The classical 1884 fiction Flatland contains a dialog between the square and the sphere, where the former tries to convince the latter that if Spaceland exists, then there must also be a space of four dimensions and a being living there made of multiple spheres in one.
In the novel And he built a crooked house by Robert A. Heinlein, an architect builds a 3-dimensional house made of 8 cubic rooms arranged according to the template of the faces of a tesseract. During the visit of the house, an earthquake actually folds the rooms and the protagonists end up trapped in what is now the surface of an hypercube.