On Cubeness: A Study

Recently, I was pondering the pleasantly stocky proportions of the the PC-FX and began to wonder how one could go about quantifying this delightful quality and, in doing so, declare the scientifically most (and least) cubic consoles. Thus, this investigation ensued:


A selection of 53 consoles and the dimensions of an associated bounding rectangular prism was compiled. Consoles were selected first based on which had readily available dimensions at [dimensions.com](https://www.dimensions.com/) and then based on a personally selected sample of additional consoles with dimensions that could be researched with some degree of confidence via Google. I devised a "cubeness" calculation that would range from 0 to 1, with 1 representing a perfect cube and zero the theoretical "least perfect" cube (basically a sheet of paper, especially legal size paper). With dimensions X, Y, and Z, where X is the largest of the three dimensions, the calculation looks like this:

cubeness = ((X/X) x (Y/X) x (Z/X))^(1/3)

or, simply,

cubeness = ((Y x Z)/X^2)^(1/3)

The cube root is not strictly necessary for the purposes of ranking the consoles, but it did give a nicer spread to the data. Consoles plus add-ons (e.g. the Sega CD) were included when feasible. This becomes important. Also, I must address the elephant in the room: is the GameCube handle included in the calculation? The dimensions I found did not include the handle and I chose to accept this. This, of course, put the GCN at a significant advantage, and I was glad to accept this (fight me!).


Additional investigations pertaining to this data are forthcoming, though in this first post I will share the overall raw "cubeness" ranking of all consoles as well as consoles+addons:



The cubeness of the included consoles ranged from 0.36 to 0.94 with a standard deviation of 0.11, bookended by Nintendo consoles (Switch and GCN + GB Player, respectively).

Returning to my earlier statement, one can now observe why the inclusion of console addons was key--the obvious paragon of cubeness should be the GCN, and the GB player proves to be the keystone that completes the pleasing dimensions promised by its name (also, it obviously helps that the handle has been excluded, but I digress). More importantly, this just barely edged out the Ouya, which was a late addition suggested by noted video game historian Phil Salvador.

Based on this data, I would propose that the included consoles could be broadly divided into the absolute units (>0.75), the inoffensive rectangular prisms (0.5-0.75), and the long bois (<0.5), with the largest swath occupying that boring VCR-esque middle territory. Please stay tuned for additional analysis. I would also be more than happy to accept any suggestions for additional consoles to include (if you can track down the dimensions...e.g. I couldn't find the Genesis 3 listed anywhere) or trends/correlations to investigate.

On seeing that the gamecube GB player = the most cuboid, what I‘m wondering is could a combination of two or more other consoles, even if they don’t interact as hardware, surpass the GCN + GB player as ideal cube shape

I'm a little confused by your formula. X/X is 1, so the whole formula would always be greater than 1, right? Obviously your results are all between 0 and 1, so is there some other step you forgot to mention?

Edit: I swear there were plus signs there before, but maybe I just misread it

@“saddleblasters”#p142509 I‘m seeing the edited version, and I’m still not entirely clear on why X/X needs to be in the formula, given that it's always 1. Perhaps accounting for the same formula as seen through the Y or Z measures, or approaching this through other cubic measures like volume or surface area (all normalized to a unit cube, of course), would do the trick.

Edit: Wikipedia to the rescue!


Applying the space diagonal formula to a cube, it stands to reason that, with all sides being equal, its space diagonal would be the square root of 3a^2 - which, with a little algebraic shuffling, works out to a times the square root of three. ~~I didn't have to check that last part against the Wikipedia page for cube, honest.~~ Therefore the closer to a cube a given console is, the closer its space diagonal comes to three times the square root of a. What exactly is a in this context? In this context, probably the longest side, since that's the side you'd have to scale down the most to get the console to fit in a unit cube.

@“saddleblasters”#p142509 you weren’t mistaken, I totally botched the formula the first time I typed it lol…not sure why I decided to rush this while waiting for my plane to board at ohare. Should have chartered a private jet with @yeso

@“Video Game King”#p142512 yeah, x/x could be simplified to 1, just left it in for clarity

@“yeso”#p142508 four series Xes. A series X is 15x15x30cm and four of them together would make 27000cc of gaming cubeness. They'd be about the size of this magic cube.


would a stack of interlocking PS4's work? Pro or base, or perhaps some combination of the two models?


@“yeso”#p142529 the front and back faces of every PS4 model are angled so you'd wind up with an oblique prism.



@“connrrr”#p142525 thank you, you just saved me so much work :joy:

what about something like this



@“connrrr”#p142533 the front and back faces of every PS4 model are angled so you’d wind up with an oblique prism.

Just apply [Cavalieri's principle](https://en.wikipedia.org/wiki/Cavalieri%27s_principle).

PS5 is more cubic than PS2? I'll have to bring that up next time someone complains about the shape of it.

@“Tradegood”#p142544 I think it's because the PS5 takes up more space on the Z axis, while the PS2 is comparatively thin

Is that essentially what's being measured here, if I understand correctly, how much of an cube shape the console fills up?

I‘d believe it! It’s a pretty beefy sandwich of a console, especially with the CD drive. I can imagine the digital version is more po'boy shaped.