The mere notion of a dichotomy is straightforward: a dichotomy is a classificatory scheme for a kind of object which represents the situation of an object between two idealized extremes. However, the scheme itself, and the situation space, can vary between dichotomies. I'll give a couple of examples:

Simple Dichotomies

We'll call any dichotomy that is used by situating instances at some place along the dichotomy, a simple dichotomy. For simple dichotomies, the primary classifying factor is the data corresponding to the situation space: with light/dark, this data is a single dimension, though it may be "fuzzed" by the complexity of our perceptive faculties; in such a case, we speak of a simple linear dichotomy, and with male/female, this data has multiple dimensions, in which case we speak of a simple multidimensional dichotomy.

Do not think that linear and multidimensional are opposites, though; the opposite of linearity is rhizomaticity. A simple rhizomatic dichotomy is one for which no internal structure, such as a straight line or multiple dimensions, may be elucidated. In such a case, we can only really use the idealized extremes to reflect more on any given instance, without placing that instance within the dichotomy. Of course, totally rhizomatic dichotomies are hardly of any use, and rare to see; the living/nonliving dichotomy, as applied to e.g. viruses and whatnot, is the closest thing I can think of right now (and it's only like this due to a lack of clarity about what constitutes life, though I wouldn't be surprised if it remained so under most reasonable definitions of "life"). To discuss this further, though, I'll need to introduce the next kind of dichotomy.

Complex Dichotomies

By way of an abstruse example:

We'll call any dichotomy that is used not by situating instances at some place along the dichotomy, but instead by analyzing the interaction of the two idealized extremes in instances, a complex dichotomy.

The dichotomy of simple dichotomies, which has at either end the simple linear dichotomy and the simple rhizomatic dichotomy, is a somewhat (but not totally) complex dichotomy. Simple multidimensional dichotomies are an example of an interaction between linearity and rhizomaticity, as multidimensionality in the abstract is just bundles of linear relationships (see the example of physical sex).

Note: it is true that we may consider simple binaries, where no intermediate can even be conceived, and that this gives a simpler structure than linearity. I considered considering the linear-rhizomatic-binary trichotomy rather than the linear-rhizomatic dichotomy, but found that it didn't change much, as the property of being binary is, ontologically speaking, so easily destroyed; once destroyed, we can only really speak of it as a statistical model, as we do when we seek to sex organisms as either male or female, statistically assuming that one immediately observable sexual trait will allow us to infer others. There's plenty of interesting things to say about this, but it's irrelevant to this.