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Premise

The task is to explain how a planet can possess cube-shaped mountain ranges and maintain them across geological time scales. I have tossed around several ideas, such as creating a vacuum around the mountains. While none of these ideas worked out, I was able to construct a list of some of the main issues with cube-mountains:
  • Atmospheric weathering
  • Tectonics (plates colliding creates pointy mountain formations)

For a moment I had resigned, thinking it was too difficult to explain with natural phenomena. Then this photo reinvigorated my efforts:

enter image description here

This site in South America is by no means the norm for planet Earth; it even remains a bit mysterious. Nonetheless, it serves a proof of concept: there can be natural processes that counteract other natural processes which would otherwise result in pointy mountains.

Question

If we aim to have an entire world where cube-shaped mountains are the norm, then what natural processes need to be in place to maximize the likelihood of cube-shaped mountains, planet-wide?

Further Clarifications

  • Interested in the long-term, if the mountains need to be pointy in the beginning, that's permissible
  • Slightly less compromising with regards to shape, the success metric needs to be near-cube in shape -- not just non-pointy (normal weathering will flatten sharp peaks)
  • Planet characteristics: to start with, but can add elements from exoplanets if needed.
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  • $\begingroup$ That's Mount Roraima, Venezuela - not Brazil. Also it's more of triangle than a cube: peakbagger.com/peak.aspx?pid=8684 $\endgroup$ Dec 28 '20 at 2:50
  • $\begingroup$ @SurpriseDog Thanks, edited for accuracy $\endgroup$ Dec 28 '20 at 3:08
  • $\begingroup$ Does the cube have to be vertical? If an "upthrust corner" is acceptable, that may be easier. $\endgroup$
    – Anon
    May 4 at 3:01
  • $\begingroup$ @Anon I believe vertical cube shaped mountains are the name of the game here, seeing as if offset at an angle it would be more or less a normal-looking mountain. Would be open to the possibility though if I'm missing something. $\endgroup$ May 6 at 6:25
  • $\begingroup$ @Arash Howaida You missed nothing. Whether these cubes had to be recognised by aliens, or were for ecological partitioning (a "lost world" on top) might affect what's viable. An upthrust edge or corner gets around the question of the angle of repose, and might be big enough to be useful depending on your requirements. $\endgroup$
    – Anon
    May 6 at 6:45
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The easiest way to accomplish this would be some geological thrust function that produces sheer cliffs, like a convergent plate margin. However, this might not produce exactly cubic-shaped mountain, because you would have one end with a sheer cliff but that end would gradually taper back down into the earth, rather than having a random cube sticking out of the ground.

Your problem isn't geology, but physics. All materials have what is known as the angle of repose, which is the steepest angle a loose pile of any one material will form when allowed to aggregate under gravity. Above this angle the downward force of gravitational pull is greater than the frictional force keeping the material together, and so the material will slump down and redistribute until the material is in a pile of the appropriate angle. This is why mountains are triangular or dome-shaped.

Under Earth-like conditions the angle of repose for most material is at a maximum of 45 degrees. I don't know how extraterrestrial conditions would alter this, but I doubt it would be possible to have a pile of loose debris achieve a pile of 90 degrees (which you would need for a cube-like slope) unless you were outside of a planetary gravity well and in outright microgravity.

Alternatively... enter image description here

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  • $\begingroup$ Devil's Tower. The question is what crystalizes into cubes instead of hexagons. It slopes but you will find smaller samples in the surrounding area that look like a level from Q-bert albeit hexagonal. $\endgroup$
    – Mazura
    Dec 28 '20 at 11:21
  • $\begingroup$ @Mazura Devil's Tower is a) ovoid, and b) a volcanic plug. It forms when a volcano gets plugged up, the magma hardens, and then the surrounding slopes of the volcano erode away. The sides don't slope yet because the rock is super-hard and sticks together, but eventually it will erode to form a talus slope. The hexagonal cracks mostly form because geological cracks often form triangular, hexagonal, or pentagonal shapes. Volcanos don't erupt as cubes outside of Minecraft. $\endgroup$ Dec 28 '20 at 13:57
  • $\begingroup$ Kudos to OP for a nice photo. I'd offer upload.wikimedia.org/wikipedia/commons/1/1f/… as one way that a cubic structure could be laid down. $\endgroup$ Dec 28 '20 at 14:29
  • $\begingroup$ @MarkMorganLloyd I think you may have responded to the wrong comment. $\endgroup$ Dec 28 '20 at 17:36
  • $\begingroup$ @user2352714 I don't, it's this answer that considers things that crystallize and under the circumstances I still think that a quick acknowledgement of OP's photo isn't too OT. $\endgroup$ Dec 28 '20 at 18:22

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