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In 3D space we can envisage one object that contains all of our objects defined by determinants.  If we take a 2x2x2 cube, we have 8 elements, these are formally the 8 elements of the geometric algebra, e,  e_1, e_2, e_3, e_{12}, e_{23}, e_{31} and e_{123}. this is a 1x1 scalar, 3 1x3 vectors, 3 3x3 matrices and 1, 3x3x3 tensor, which together make 64 units, a 4x4x4 cube. Thus the arrangement would be to have one corner as e, then the 3 axes running from this corner to be e_i, then the 3 planes between each pair of axes e_{ij}, leaving a shell around a box which is \epsilon_{ijk}.