Oh boy didn't even notice when a year on SteamGifts has passed. Lured here by 25k Faerie Solitaire giveaway, had only 3 games on my Steam account and was even 3 cents short to join (back then the threshold was $50). Deus Ex was having a sale so figured, why not. And the rest is history, eh? By now between Steam sales, indie bundles, SteamGifts and generous friends I passed 666 games on the profile (though barely 420 in the library i.e. not counting DLCs, demos etc).

What a year it was!

And what a sweet curse of abundance it is xD

I like to think that I'm known at least in the established puzzling community around here and that my puzzles are well regarded by connoisseurs, though sometimes may be on the harder side. Puzzles were my main source of entertainment and wins around here so sometimes I need to stir up that part of community to keep the ball rolling :3 But I admit I'm not all that active lately so won't blame you if you don't know me :P

Anyway, what better way to celebrate than with a puzzle, then. Sorta. I've been keeping myself busy lately so didn't have time and/or will to cook up something harsher, so this is a solid quiz with little to no puzzling involved. Well, maybe a bit. Wouldn't be me if I didn't at least try to confuse you occasionally, especially with flood of words, but generally this is something I don't usually do: relatively straightforward quiz on itstoohard.com.

So, a solid quiz. Incidentally, it is also a quiz about solids.

SOLUTION

The OP had a wall-o-text mostly to discourage tl;dr folks but of course had some relevant info as well, besides making sure you understand you are supposed to solve this solo. Most notably, that the whole thing is an itstoohard.com quiz and what is the code to the puzzle (joBARU7M). Trained eye probably could've picked it up without reading, still xD

Some useful info was that it is generally about convex polyhedra (but as you will see, generally doesn't mean always) and that I generally don't accept multiple answers (actually often I did but wanted you to focus more on the answer, that I want something specific to the situation, not too generic, but still scientific). Also mentioned about D12 die as a quite heavy handed hint to a question later on about D24 (was threatening not to accept multiple answers but actually I did accept 2 distinctly different answers for that one). But also that you should not try to be, so to speak, too carried away with defining exact shape because sometimes you're going to ignore some small unimportant features.

Solid quiz.

Q1. Detective work.

I didn't really expect you to know the answer but I provided enough background info for you to find out this was about Freescape engine, and the game was Driller. It takes place in a penitary mining colony consisting of 18 square platforms encompassing a moon. Gas is building up under the platforms and you gotta place mining rigs on each platform to release enough gas, or else whole moon blows up, taking the nearby planet with it. Really nice enviromental puzzle game (as in you need to properly navigate the 3D environment and gather clues where to put your mining rigs).

The 18 platforms form the shape of (small) rhombicuboctahedron (kinda like cube and octahedron were having at it together). Triangles actually were holes, you would fall on the surface of the moon and be killed by a "scanner" iirc, but never mind that.

So one of the accepted answers would be rhombicuboctahedron, thanks for question #1!

Further down the line let me ignore the "thanks" when providing answers, mkay?

But also permitted were small rhombicuboctahedron or elongated square orthobicupola. I know, despite threatening to accept only one answer xD

Q2. Yes, it's called football.

Indeed, the most popular sport, globally, is (association) football, and, surprisingly, the eponymous object is an actual round ball that is actually kicked by actual feet as actual normal game mode. You know, football.

Now obviously this is a ball/sphere (not prolate spheroid like in some other sports called football) but a traditional design is a spherical polyhedron, which (ignoring the inflation/pressurization) is based on Truncated icosahedron.

Q3. Life goes on.

Pretty f*ed up tragedy indeed. For what it's worth, the new building nearly at its completion is rather pretty. Talking about One World Trade Center (I understand they don't call it Freedom Tower officially but I don't know what Newyorkers think) and 9/11, which was year 2001.

Which yes, it was the first year of 21st century of Gregorian Calendar (chances are you use this calendar normally.. it is sort of a global standard, but many areas actually have their own calendars). In case you live under impression that 21st century started in 2000 you are wrong (there is no year zero, centuries go 1-100, 101-200, ..., 1901-2000, 2001-2100). So a bit of confusion maybe and hopefully learning experience in case you were under wrong impressions. So sad that people celebrated 31st Dec 1999 like a new century is starting. Year too soon.

Anyway, as even the wiki article tells you, it's a square antiprism.

Q4. Never forget.

OK so what was the shape of one of the original Twin Towers? You might have gotten successfully confused by now but the answer is rather simple: square cuboid. Pretty much majority of buildings are cuboids but those two had a special type, with square base.

Also accepted square prism and right square prism.

Q5. Solid quiz - or a puzzle?

I mean... really? Solid water? Google these two words together: solid and water if you don't know the answer. What comes up? Really, it's that simple. I'm not looking for Platonic interpretation of essences. I'm looking for solid water (solid as in adjective not a noun). Water itself has no shape. I mean.. you want to go to molecular level? When it becomes solid I guess you may start talking about crystalline structure but well you probably don't refer to it as water then anymore anyway, and the answer is much simpler. Also stuff you add to beverages may be called a "cube" even if it isn't really a cube, but that also obviously was not the answer.

I mean, really? You still want me to give you the answer? Ice. Surprising, how minds can be misdirected and overthinking.

So yeah bit of a tricky question to keep the notion of puzzles/riddles going as opposed to "google this" trivia. Even though google would help you too :P

Dual polyhedra quiz

Solid quiz didn't lead to a giveaway, but to another, final quiz. Title is important and description stresses that, too. Questions were actually asking not about the apparent polyhedron, but about its dual.

Q1. Die.

So yeah initial description was mentioning D12 die and this is about D24 die. I actually accepted two shapes, despite my threats: deltoidal icositetrahedron and tetrakis hexahedron. Which led to dualistic answers of good, old rhombicuboctahedron or truncated octahedron.

Also accepted other variants of rhombicuboctahedron, small rhombicuboctahedron or elongated square orthobicupola.

There are some other variants on D24 but at least partially my threats were fulfilled.

Q2. A twist.

This had quite literally a twist. One could think it is again your good, old rhombicuboctahedron but as a matter of fact it isn't. The net is for a solid that is similar, but one of the square cupola is rotated a bit and it forms pseudorhombicuboctahedron (or in other words, instead of elongated square orthobicupola this is actually elongated square gyrobicupola). Hooray for twisted pun!

Now there's something special about this question which could make you paranoid. Realizing that J37 is Johnson solid number 37 so this is a hint to the question could quench your paranoia, but... Are you sure you shouldn't be more paranoid about such unusual occurence?

But anyway again the answer is actually the dual polyhedron of the one that net is displayed, so: pseudo-deltoidal icositetrahedron (for good measure also pseudodeltoidal icositetrahedron or pseudo deltoidal icositetrahedron).

Q3. Defiant Joe.

Hm I was so certain it's very obvious what I am looking for that it didn't occur to me that some people may jump to conclusions slightly too soon (kinda my bad) and focus on that first shard thing (some elongated bipyramid?). Actually let it roll bit more and you'll see big blue "ball" which actually is rhombicosidodecahedron (well at least I assumed so; for all I know this could be, say, gyrate rhombicosidodecahedron or some other Johnson solid variation, but let's keep things simple).

That led to (dual) answer deltoidal hexecontahedron, or alternatively trapezoidal hexecontahedron, strombic hexecontahedron or tetragonal hexacontahedron. Yeah, I did accept some variety in the end.

Paranoid Android.

As you can see in the comments below Marvin wasn't paranoid enough to attempt entire quiz (seems so at least), but for those who were, there was extra paranoid challenge added. One of the quizzes had a hidden giveaway. Though only place I mentioned it was the giveaway you got by solving the quiz, although that one particularly funny thing about one question might have raised some red flags that something is not quite right, especially that there's one more private giveaway visible on my profile. But yeah usually it's good not to be too paranoid. The stuff was hidden in the one image on the quiz.