Pedro de San Patricio
Gold Member
Dimension in this context is directionality. A point is a 0D space. Directionality isn't an applicable concept in its case. A line is 1D and includes two directions along its one axis. A square is 2D. You can move along both its axes and to any point between them. A cube is 3D. It's much like a square but includes the concepts of up and down and another axis of freedom. A tesseract is the next logical step. It is a 4D object and includes yet another axis enabling movement in directions we can't totally comprehend. This is why we find it impossible to visualize exactly what a 4D object, such as a tesseract or a dodecaplex, actually looks like.