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In an interstellar competition the best LEGO world builders have gathered in all galaxies. They are the best builders that have emerged from inter-planetary competitions throughout the universe. Every galaxy can send the best builder to the universal competition, to be held around the planet of the previous winning builder. The aim is to built statues of the local leaders of the planetary systems.

As the structures built are huge and as it is expected to be even larger than last time (expectations are they will have the size of about the Earth!) new bricks must be supplied.

How strong must the bricks be and what will be the best internal structure to achieve this? Will solid bricks be the best? Graphene based bricks maybe?

Assume normal sized LEGO bricks. The structures can be built top-down or down-top. Would this make a difference? Will there be a size for which the structures collapse? So they can't be finished?

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    $\begingroup$ It doesn't matter. If you put enough pieces in the shape of Lego bricks together to accumulate 12,000 billion billion tonnes, it is irrelevant of what material they are made: under that gravitational force any material behaves like a fluid and the heap of Lego bricks will take a spherical shape. $\endgroup$
    – AlexP
    Aug 4 '21 at 11:00
  • $\begingroup$ What if you make a hollow sphere? $\endgroup$ Aug 4 '21 at 11:05
  • $\begingroup$ That condition should be in the question, and the structure would not be a planet-like world. (And the competition would be quite uninteresting. In the limit, you can make the "bricks" infinitely thin, so that the "structure" is just a massless arbitrary sphere of outer space vacuum. You need to add additional rules, such as what is the required load-bearing strength of the structure.) $\endgroup$
    – AlexP
    Aug 4 '21 at 11:08
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    $\begingroup$ Gravity seems more likely to be the thing that will rip the structure apart, not bind them together, unless (as has been suggested) it's actually a planetary mass of faux-Lego, in which case it will be ripped apart and reassembled into a ball. $\endgroup$
    – jdunlop
    Aug 4 '21 at 17:22
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    $\begingroup$ Faux Lego would be Lego made of materials (like diamond) which couldn't adhere to the Lego Group's stringent rules w/r to "clutch" (deformation and friction adherence) and other properties of the bricks. I suppose in the distant future they could've changed their tune, but they've been very firm on the rules since the 60s. $\endgroup$
    – jdunlop
    Aug 4 '21 at 17:51
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Let's assume that the lego bricks are about a centimeter tall and four centimeters long, for a surface area of 4 centimeters squared.

They need to cover a cube about 10,000 kilometers wide. The surface area is about 600 million kilometers squared.

By basic calculation, we can see we need 6*10^18 lego bricks. A lego piece weighs about a gram. So, the lego structure will weigh 6x 10^18 grams, or 6x 10^12 tons. This is the mass of around 20 Mount Everest's.

Even including support structures, the mass isn't close to large enough to have a notable gravitational pull, given their small size compared to say the moon, which weighs around 10 billion times more. At the distance of the moon, the planet will have more gravity than the statue.

You'll still want some internal stabilization thrusters of course, to handle solar winds and the flexing gravity causes. Since part of the fun is the risk of it falling, there could be some limits set by whoever did the contest to how many thrusters you have, ensuring that much of the balancing has to be internal.

You'll also need some radiation shields, to block micro meteors and such from damaging it. These could be small enough to not be visible from the planet.

You'll probably want some fairly tough carbon allotrope like diamond, because space is a fairly harsh place. One with the toughness of diamond but less chance of fracturing. It's a competition, so some people will probably choose heavier more solid bricks that are more resistant to external forces and some will probably choose lighter bricks that are easier to move around with thrusters.

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  • $\begingroup$ What if the game is held around a Lagrange point? $\endgroup$ Aug 4 '21 at 13:53
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    $\begingroup$ You could do that, but there are a lot of external forces so you'd still need some thrusters to keep it from flexing apart. They're about 50 times as large as the earth, so lots of space for statues. They're also ten times further away than the moon, at a minimum, so they'd be harder to see from the planet. $\endgroup$
    – Nepene Nep
    Aug 4 '21 at 14:02
  • $\begingroup$ Thats clear! Almost accepted. I still wait a bit. $\endgroup$ Aug 4 '21 at 14:05
  • $\begingroup$ Worth noting that if you change the material from ABS plastic to a carbon allotrope, your mass calculation will have to change as well. $\endgroup$
    – jdunlop
    Aug 4 '21 at 17:55
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    $\begingroup$ The mass calculation is meant to be fairly rough. You're 10 orders of magnitude away from having as much mass as the moon- you're quite a way away from having to focus on the details. $\endgroup$
    – Nepene Nep
    Aug 4 '21 at 17:57
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An object as big as Earth is defined as a planet, meaning it is a body under hydrostatic equilibrium. What does that mean? It means that the internal forces of the body overcome any material resistance and shape it like a sphere.

And if that happens for rocks like iron or granite, there is no Lego which can stand the load and keep its shape. No matter what shape you give it, after a while it will crumble under its own weight.

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    $\begingroup$ @DescheleSchilder, any shape will turn into a sphere. Potatoids don't grow that big $\endgroup$
    – L.Dutch
    Aug 4 '21 at 12:13
  • $\begingroup$ Potatoids. Thats a good one! What about pentagramoids? $\endgroup$ Aug 4 '21 at 12:55

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