The cabinet shape can make a difference, even if the enclosed volume is exactly the same. While the panels may be acoustically dead, the air space within is not. The enclosed volume should never have two internal dimensions the same (such as top to bottom and front to back) as that will usually reinforce standing waves at certain frequencies. The air within the box can be made somewhat acoustically dead by adding damping material - fibreglass 'wool', or any number of proprietary filling materials that are designed to absorb the sound inside the enclosure. You'll find claims (well, perhaps not quite) that only virgin yak's wool should be used, because man made fibres 'sound bad'.
When these materials are added loosely, the effect is to make the enclosure acoustically larger. If packed in tightly, the enclosed volume is smaller. Both of these change the way the loudspeaker driver reacts with the enclosed volume, mainly at or near the speaker's resonant frequency. In many (but I suspect by no means all) commercial designs, it's expected that the driver interaction with the filled volume will be modelled and measured, and the filling adjusted to get the right amount of absorption, while minimising internal reflections to the point where they can 'do no harm'. Even this term will be variable - some will claim that -40dB is ok, others may insist on at least -60dB, while others might be content with -20dB.
Many people design cabinets with the deliberate aim of avoiding all parallel surfaces. This prevents (or helps to prevent) standing waves from developing within the enclosure, and is generally a good idea. However, it's not easy to do without dedicated machinery that can cut precise odd angles so that it all fits together. In some cases, you may find that adding an internal baffle at an angle within the enclose space will work, and if it's well perforated (to ensure that the total internal volume is available to the rear of the speaker cone) it may be enough to prevent major standing waves. Acoustic damping material is still needed, no matter how irregular the interior volume. The idea in most cases is to absorb the rear radiation from the speaker completely, because any sound that re-emerges through the cone will not be in phase (or in time) with the original.
I do not suggest or recommend commercial software used to design speaker enclosures, with the one exception of the free program WinISD (you can find it on the Net). There are countless programs that either do (or purport to do) complete designs, based on the drivers you are using. These omissions are not because the software doesn't work, but simply because I operate as an independent individual, and I do not make specific recommendations for anything, other than components used in project articles.
This is probably the most common enclosure in use today. It was used in very early speaker systems, but it was basically a 'trial-and-error' design until the loudspeaker parameters were properly quantified by Neville Thiele and Richard Small. This allowed mathematical calculation of the enclosure and port sizes, and it was then possible to design a system, build it, and have it perform as expected. Many of the early 'tuned' boxes were what's now commonly referred to as 'boom boxes', because they had excessive and often 'one note' bass. Countless programs have been written to allow users to design an enclosure, based on the Thiele-Small parameters. This has removed much of the guesswork, but by themselves, the programs are (mostly) unable to provide a complete design. Most provide the necessary internal volume and port (vent) diameter and length, but further 'tweaking' is nearly always needed.
An aperiodic enclosure is (kind of) halfway between a sealed and vented box. The vent is deliberately restricted, so it's either a leaky sealed box, or a 'constricted' bass reflex. There's quite a bit of information on the Net, but not all of it is useful, and design equations are hard to come by.
The above is one of many different ways that an aperiodic enclosure can be configured. This isn't a technique that's widely known, and it's also not one I've experimented with. Many claims are made, and there are many variations - in some cases, just a small hole or a series of narrow slots is used, with appropriate damping material covering the openings. There appears to be little consensus from designers, so the technique is somewhat experimental. It's claimed that with an appropriate aperiodic 'vent' that the enclosure is made to seem much larger than it really is, and it's not uncommon to see aperiodic enclosures that appear much too small for the driver used. As I said, I've not tried this approach, but may do so when time (and motivation) permit.
Isobaric enclosures can be used with or without a vent, depending on the desired outcome. Most speaker design software can accommodate isobaric configurations, but the mechanical details can be awkward to produce. There are some commercial isobaric enclosures, but they aren't especially common in the market. This is a good design to use if the driver you wish to use requires a box that's larger than you can accept, but no isobaric enclosure should normally be operated above around 300Hz or so. The cost, weight and relative inefficiency of isobaric enclosures limits their usefulness for commercial systems.
These are without doubt the hardest to design, and even small variations from the 'ideal' can cause serious response anomalies. Because of the acoustic filter, some people will say that this enclosure type is responsible for 'day late' bass - there is often a significant delay from the application of a signal before the resonance is stimulated sufficiently to produce output. The delay is usually somewhat less than a full day, but you get the idea . This configuration can be extended to eighth order, but this is less common (and has a very narrow bandwidth).
Finally, there's the transmission line. In theory, the idea is that the line is infinitely long, but this is a little impractical for most listening spaces . Mostly, the line is designed for wavelength at the speaker's resonant frequency, and there will be some reinforcement from the open end of the line. These are notoriously difficult to get 'just right', and the process usually involves experimenting with stuffing within the transmission line until the desired outcome is achieved. An optimally set up transmission line should reduce the resonant frequency of the driver, something that no other enclosure type can achieve.
Because the design of horns is so specialised, this is the limit of what is shown here. However, construction methodology, the need to ensure that panels are not resonant and other general comments apply to any enclosure, regardless of the type of system. Panel resonances in a folded bass horn can be particularly troublesome, due to the high pressure at the throat of the horn.
Many manufacturers are now using advanced composites, which let them create any shape relatively easily. Cellulose reinforced resins and 'exotic' plastic resins are common, but the requirement for moulds to create the finished shape (and an autoclave to cure the resin) means that these are generally not suited to the DIY approach. It's not impossible of course, but even getting the materials in small quantities may prove difficult. 'Traditional' materials will almost always be the best choice for DIY, because an enclosure can be built using only basic hand and power tools.
Remember that it's the outside of your enclosure that needs to look good. The internal construction with angled braces and odd shapes is not visible, and should be designed for rigidity and performance, not appearance. Deadening materials (e.g. bitumen tiles, heavy felt or other mass-damping treatment) needs to be very well bonded to the interior of the treated panels so it cannot move, rattle or fall off. All internal wiring has to be secured properly to prevent rattling as well, because it can be very difficult to correct after the box is sealed up and you only have access via the speaker cutouts.
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