an alternative approach to dimensionality

I feel like I may have written about this before, but regardless, I am going to write about it here and now.

The 3 (or 4 including 0) physical dimensions that we are all familiar with have always bothered me. The distinctions between them seem inconsistent, like there is something missing. The numbers don't seem to correspond to what they describe. I would like address this by proposing my own dimensional distinctions. Instead of asserting 4 dimensional distinctions, I will propose 5.

--Note: none of this has anything to do with time being a dimension or with string theory, I am only concerned with the physical dimensions that we generally consider when we talk about dimensions--

So, the first distinction is 0. In the current model, a zero dimensional object is a point. But why would we begin with anything at all? Since zero is the numerical description of nothingness, then why doesn't the zero dimension describe the environment of nothingness? Although it wouldn't come in handy too often, it's certainly an important distinction to make. Zero dimensions denoting the possible existence of anything, even just a point, seems counterintuitive. So in my model, zero dimensions is nothingness--a complete lack of anything and the lack of any possibility.

Now my zero dimension is really the only addition to the current system. Everything else shifts upwards. The zero dimensional point becomes the one dimensional, which makes sense since a point is always singular and is the only thing that can exist in that dimension. The first dimension becomes the second dimension which is a line or line segment. This makes sense because a line is the connection between two points, so two points exist in two dimensions. Then the second dimension becomes the third where the triangle is the simplest form (three connected points). And of course, the third dimension becomes the fourth where the tetrahedron is the simplest shape (yes, 4 connected points).

I do understand that the original dimensionality distinctions were based on axes (as in the plural of axis), but why? An axis is a device for understanding forms. In the end dimensionality is also a device for understanding forms, so why not let the distinctions be based on the forms themselves instead of letting one device determine the nature of another? Under the current system, there is an implicit assertion that axes somehow exist before dimensionality ('a priori' for you latin readers). In fact, they are coincidental because they are both human contrivances used to place forms into a useful schematic. I believe that whenever possible, the schematic tools we use to deconstruct forms should be derived from the forms themselves. This will prevent our approach to understanding forms from becoming unintuitive and convoluted.