In the 19th century the mathematicians Gauss and Riemann studied multidimensional spatial structures and discussed the question of whether there is a 4-dimensional space in which a 4-dimensional cube can be represented without distortion. In his novel Flatland (A Romance In Many Dimensions) Edwin A. Abbott writes about this relativity of reality. He describes a surface-world and the attempt of a 3-dimensional body (a sphere) to explain the third dimension to a 2-dimensional irregular hexagon.
The fascination with 3-dimensional representations of n-dimensional orthogones reveals itself on closer examination of these objects. One begins to discover complex and idiosyncratic structures. Crooked dice, unknown bodys ... The thought that there "really" is fourth, fifth, sixth... spatial dimension seems less abstract and more mysterious, if you do not look at mathematical rows and formulas but concrete structures.