In endeavoring to design a true 4-dimensional house, we must first, as might be expected, concern ourselves with questions of mathematical definition. The foremost among them being: what precisely is a Tesseract or a Hypercube? In mathematics it is easy to define four dimensional geometry. From this point of view it is also quite easy to describe what shape (or shapes) in our real world a Hypercube can assume. In the architect's imaginary, on the other hand, a tesseract (architecture) could be either a building whose shape looks like one of the infinite configurations the hypercube can assume in its spatial developing; or else, we can try to get and reproduce the core of four dimensional geometry. Living inside a tesseract can be a very simple way of explaining a complex concept, by means of our limited but developing perceptual skills, or a very complicated way to describe a not so difficult idea, in a narrative sequence of concurrent spatial events. A clever architect in a novel by Robert Heinlein designs a house in the shape of the 3d unfolded vertical tesseract, but it collapses (through the 4th dimension) when an earthquake shakes it into a more stable form. So, if we were Quintus Teal, the "graduate architect" main character of Robert Heinlein's novel "And He Built a Crooked House" [1], what kind of folded, reversed, house should we observe and eventually, from that revolutionary event on, could conceive and design? © Institute of Mathematics and Physics, Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava.