> the building will fit along each coordinate inside the diagonals, but the edges of the hypercube would still cut through the building, right? No, you can fit

> the building will fit along each coordinate inside the diagonals, but the edges of the hypercube would still cut through the building, right? No, you can fit the whole thing inside the 1mm hypercube, as long as you have enough dimensions. Once you have fit the height of the building along one diagonal, you can add new dimensions and rotate the building along that diagonal so that the width and the height will fit along the diagonals of the other dimensions.