Aromaticity is a fuzzy subject and there are no strict mathematical rules. There is no recognised unilateral theory that does explain it. This becomes a real issue when we are dealing with compounds that are generally hard to describe. One such compound is 1,4-dioxin.
This makes it a very unfortunate battle ground for dogma, which the answer provided here and comments following are proof of. You cannot draw a line and multiple textbooks have published and teached a romanticised version of this topic. It is way more complex than drawing a molecule and counting π-electrons (which strictly do not exist but are rather electrons in π-orbitals).
The Gold Book defines aromaticity (https://doi.org/10.1351/goldbook.A00442) this way:
The concept of spatial and electronic structure of cyclic molecular systems displaying the effects of cyclic electron delocalization which provide for their enhanced thermodynamic stability (relative to acyclic structural analogues) and tendency to retain the structural type in the course of chemical transformations. A quantitative assessment of the degree of aromaticity is given by the value of the resonance energy. It may also be evaluated by the energies of relevant isodesmic and homodesmotic reactions. Along with energetic criteria of aromaticity, important and complementary are also a structural criterion (the lesser the alternation of bond lengths in the rings, the greater is the aromaticity of the molecule) and a magnetic criterion (existence of the diamagnetic ring current induced in a conjugated cyclic molecule by an external magnetic field and manifested by an exaltation and anisotropy of magnetic susceptibility). Although originally introduced for characterization of peculiar properties of cyclic conjugated hydrocarbons and their ions, the concept of aromaticity has been extended to their homoderivatives (see homoaromaticity), conjugated heterocyclic compounds (heteroaromaticity), saturated cyclic compounds (σ-aromaticity) as well as to three-dimensional organic and organometallic compounds (three-dimensional aromaticity). A common feature of the electronic structure inherent in all aromatic molecules is the close nature of their valence electron shells, i.e., double electron occupation of all bonding MOs with all antibonding and delocalized nonbonding MOs unfilled. The notion of aromaticity is applied also to transition states.
Please note that there is no mentioning of the Hückel (4n + 2) rule and no mentioning of antiaromaticity.
The IUPAC Gold Book gives us another definition under the term aromatic (https://doi.org/10.1351/goldbook.A00441):
- In the traditional sense, 'having a chemistry typified by benzene'.
- A cyclically conjugated molecular entity with a stability (due to delocalization ) significantly greater than that of a hypothetical localized structure (e.g. Kekulé structure) is said to possess aromatic character. If the structure is of higher energy (less stable) than such a hypothetical classical structure, the molecular entity is 'antiaromatic'. The most widely used method for determining aromaticity is the observation of diatropicity in the 1HNMR spectrum.
See also: Hückel (4n + 2) rule, Möbius aromaticity
- The terms aromatic and antiaromatic have been extended to describe the stabilization or destabilization of transition states of pericyclic reactions The hypothetical reference structure is here less clearly defined, and use of the term is based on application of the Hückel (4n + 2) rule and on consideration of the topology of orbital overlap in the transition states. Reactions of molecules in the ground state involving antiaromatic transition states proceed, if at all, much less easily than those involving aromatic transition states.
Finally, we need to look at the definition of the Hückel (4n + 2) rule (https://doi.org/10.1351/goldbook.H02867):
Monocyclic planar (or almost planar) systems of trigonally (or sometimes digonally) hybridized atoms that contain (4n + 2) π-electrons (where n is a non-negative integer) will exhibit aromatic character. The rule is generally limited to n = 0–5. This rule is derived from the Hückel MO calculation on planar monocyclic conjugated hydrocarbons (CH)m where m is an integer equal to or greater than 3 according to which (4n + 2) π-electrons are contained in a closed-shell system. [...]
Systems containing 4n π-electrons (such as cyclobutadiene and the cyclopentadienyl cation) are 'antiaromatic'.
Unfortunately this definition also has some issues (especially the chosen terminology which I consider wrong), but I do not want to go deeper into that.
However, it must be noted that from a purely technical point of view the last sentence is misleading. Cyclobutadiene as it exists is not an antiaromatic molecule, because it avoids this destabilisation by distorting. So there is a conundrum.
For that reason, it is safer to ignore this sentence.
On the DF-B97D3/def2-SVP level of theory (and all others I have checked), 1,4-dioxin is planar. Also for all intents and purposes it does not matter whether it is perfectly planar or slightly distorted. Therefore, for the sake of this argument it is planar.
In this special case, it has D2h symmetry.
The molecule is a monocycle.
Let's have a look at the π-orbitals. In the following the blue/orange ones are doubly occupied, the red/yellow are virtual orbitals.
We can see that (in this framework) all atoms are trigonally coordinated (or bent). We can count the occupied orbitals, 4, and hence have 8 π-electrons.
From this alone, applying only the definitions, the molecule must be antiaromatic.
It isn't though.
The problem with antiaromaticity arises that two (or more) degenerate orbitals are singly occupied in such hypothetical structures and that there is at least another structure that is lower in energy that doesn't have this problem.
Let's take cyclobutadiene. If all carbon carbon bonds were the same, it would have D4h symmetry and there are degenerate orbitals half occupied. A structure with different bond lengths doesn't have resonance stabilisation, but it also doesn't suffer from the degeneracy issue. This rectangle-like structure is lower in energy than the hypothetical one that is 'antiaromatic'.
For 1,4-dioxin we do not have this problem. The orbitals are not degenerate. The two oxygen break symmetry enough so that fürther distortion is not necessary.
Here are the energies of the orbitals shown above:
25 1.135267952 Unoccupied B2G
23 -1.097443828 Unoccupied AU
22 -4.154667088 Occupied B3U
21 -6.911474284 Occupied B1G
19 -9.230446836 Occupied B2G
16 -10.846271644 Occupied B3U
Let's circle back to Hückel. This rule is best understood as a guideline to explain aromaticity after the fact. It is not a good predictive tool. Heteroatoms were not included when this rule was conceived.
Most aromatic molecules do not follow Hückel's (4n + 2) rule, but are still considered aromatic.
If an experiment says a compound lacks the characteristics of an aromatic molecule, it isn't. I do not have access to the source Wikipedia cites, but it appears to be a study on exactly that issue.