This involves a bit of metaphor.

You enter this 3D world and you are floating in infinite space, next to you is a dull gray sphere.

You click. Nothing happens.

You click again. Still nothing happens.

You click a third time and pop, a triangle emerges, with each vertex at your click coordinates (we assume no two click locations are the same).

The triangle has a crosshatching texture on its surface that suggests "unfinished". The crosshatching is dull red that seems to glow just a tiny bit.

Now you grab the sphere and move it around. You notice that your sphere passes right through your triangle.

You also notice that your mouse pointer passes right through your triangle but does not pass through your sphere.

With nothing else to do in the entire universe you fiddle around a bit more and decide to move the sphere so it's poking through the triangle just a bit, right in the middle.

As your mouse pointer won't pass through the sphere, you find you can "rest" your pointer on the sphere and click. The first time you do this, Three more triangles appear inside your triangle: A line from the each vertex of the original triangle comes to meet your click point. But wait a minute, That mid-point was raised. You've now got a tetrahedron.

Leaving the sphere where it is, you now click inside of each of the three new triangles again using the sphere as a guide*.

After many such clicks, you realize you've created a 3D mesh of triangles with little bump in the middle. "Meh", you say.

But then you switch to you de-pointer tool and knock out a few points away from the bump in the direction of one of your original three vertecies.

You re-fit your sphere into the whole you've knocked in this spider's web and make another bump in your sphere just for fun.

Now you've got a triangle with boobies. Oops.

When you right-click on your triangle you see an option "toggle to anvil". "Hm", you say and click it. Your cross-hatched triangle with the glowing hatch mark goes "psssss.." and turns the same dull gray as your sphere.

Thinking you "get the idea" you right-click on the sphere and choose "toggle to working piece". "Whhph..!", your sphere is now a bunch of triangles crosshatched with hot, radiant, glowing ink.

Giggling like a child, you knock out a place in your sphere, manuver the boobie-triangle into the inside of the sphere and make the boobies poke out.

Click-click-click... "Psssss...", your triangle is now iron gray again and has boobies.

Points and such

• "Spider web" gives me an idea. What if you're a spider in this universe and you can "click", attach your stretchy web to a solid object, or onto another piece of web. You can adjust the stretchiness, etc. You could do some of this triangle-making as a spider too.
• As you learn smithing, you could think about adding tools to "generatively" do whatever you like, in the form of commands you can create and invoke, with your universe as input.
• Maybe in addition to the eraser tool, you can just create an enclosed volume when you edit. You can chose to leave them, but if the system recognizes that there are vertices inside a fully enclosed space it can, at your whim, sweep through and remove those for you.
• Instead of "undo", how about: you can sweep forwards and backwards in time as you like and watch what you did, freeze, etc. If you want to go back "a bit" to where your mistake was, you can "fork" your universe at that point, and re-live history the way you intended. Maybe you can optionally purge that "wrong" fork (or not).
• Regarding above, with enough constraints and a clear way of "how the world works", maybe you can "replay" bits of universe from the point you are right now. Or maybe have a way to record macros, at least.

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If a ruler is a "straight edge", let a plane in our case be called a "strait plane". Of course both a plane and a line are kinds of "strait branes".