Why 18 Junctions? The Math Behind 3D Shapes Explained! #shorts

Added: 2026-05-20

[00:00:00]Let's see if I can figure out why there are those 18 and nothing else.

[00:00:07]Well, if we have three face three vertexes coming together, that means there are eight octants, right?

[00:00:15]And the stuff of the object may fill 1 2 3 4 5 6 7 or all eight octants.

[00:00:22]Now, of course, if you fill all eight octants, there's no junction, so we don't consider that case.

[00:00:27]If we don't fill any of the octants, there's no junction, so we there's no vertex, so we don't consider that case.

[00:00:33]But if just one of the eight octants is filled with stuff, then we can look at it from any of the seven remaining octants.

[00:00:43]So, right now, you're looking at it from one of the seven remaining octants, and if I'm not mistaken, you're going to see a fork-style junction there, right?

[00:00:53]And you're going to see a fork-style junction in which all of the edges are con-