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I played Horizon Wars a few times, and was interested in the use of d12 in that system. In a few interviews with Robey Jenkins, he talks about how 12 is a very good dice for mathematical reasons. I admit, I am not a mathematics guy, except for the basics required in this hobby. Complex number modeling beyond simple 2dX histograms is beyond me.

So, what makes d12 a dice of interest beyond a d10, 2d6, or some other dice?

8.33% per facing, with double the amount of granularity as the d6.

It's also got a wide face that's relatively stable after coming to a stop.

 Easy E wrote:
what makes d12 a dice of interest beyond a d10, 2d6, or some other dice?

Nothing. Absolutely nothing.

At its core, a d12 is just a fancy, expensive d6 with an optional coin flip. Probability-wise, there isn't anything that a d12 does different compared to a d6 or a d10, and it's not nearly as good as Xd6 in terms of creating normal-ish distributions.

The only reason to use d12 is because you want to be different for the sake of being different.

If he really wanted granularity, he'd have gone with d20.

In terms of game design, you have a 50% success rate on a 7+. From there, you have 5 points above and below, plus auto pass (1+) and auto fail (13+).

Compared to a d6 where 4+ is 50% with 2 points above and below (plus auto pass/fail) you are much more able to granularly represent changes in ability. It would make it easier to factor a wider range of ability. For example, a las gun with strength 3 attacks a tank with toughness 8 could be wounded on a 12, while a bolter could wound it on an 11. A plasma gun could wound on an 8, and potentially wound T12 on a 12.

I like D10's, myself, because the pointy shape gives you a natural scatter die.

One place I could see a D12 being very useful is if you had a game where rolls were on a 1-12 scale, and you used both 2d6 and d12s to make the rolls. So D12's are useful for "Double-or-Nothing actions (higher chance of rolling 10+, but higher chance of 3- as well), while 2d6 will cluster closer around 7's.

Multi-d6 (or any multiple roll) has the side effect of slowing game play, with the *benefit* of a probability curve.

In Warmahordes, I would gladly accept more random distribution of results for faster gameplay. Admittedly, it would become unit vs unit combat rather than model vs model, but I would personally love that. 75 points is a bit of a chore to roll out so many individual actions.

And yes, Boosted rolls would need reworking (+3 to the roll?) but again, I would like the faster game play with the greater granularity.

12 is a good number, cleanly divisible by 2,3,4 and 6, its a good system for determine probabilities as fractions of a whole.
You can have an 'analogue' probabilities system from this, one third chance, half chance, two thirds chance, three quarters chance, you could translate a d12 roll into something sounding more poetic than an in game determination.

I like the D12 and in my game system that I had been working on, but have been neglecting for some years now uses a D12.

My reasoning is that I can make 1 = always fails and 12 = always succeeds and still have 10 points of wriggle room in between.

Plus I like the look of the shape of a D12.