Before we can build Olympos, we have to start with empty space. Nothing. Nada. Zip. The Archetypal Newbie!

What's the first thing you can put in empty space? A single point. It's a dot with Zero dimensions and is just about useless by most standards. It's like an infinitely small circle.

That's 1 point, 0 dimensions.

And if you add a second point? Now you can see dimensional space, because with 2 points you can derive length, which is 1 dimension. You can even refer to a unit of length: the distance between the 2 points. But at this point everything is relative to the 2 points, since they're the only things that exist in the empty space. Still not much you can do, aside from exploring abstract equivalents of Zeno's paradox and stuff, like bisecting a line made between the two points, bisecting the line between the 1st point and the half-way point, etc.

2 points, 1 dimension. Line, distance/length.

In order to get to 2-dimensional space, you need a third point not placed along the line made by the first 2 points. Place this point anywhere at all in the empty space, and you are able to establish a flat plane of some kind. In fact, you can connect the points to make a triangle, no matter where you placed the three points. You can now refer in a more or less meaningful way to the length and width of the triangle. In 2-dimensional space, you can start thinking about relatively useful stuff.

3 points, 2 dimensions. Plane, distance/length, width.

Adding a fourth point not located on the plane established by the first 3 points finally gets us into 3-dimensional space. Length, width, and height may now be meaningfully discussed. You can now form a solid. Now we're getting somewhere.

4 points, 3 dimensions. Solid, distance/length, width, height.

The most basic kind of "regular object" you can make in 3-dimensional space is a tetrahedron. It uses the minimum number of points (4), equidistantly spaced from one another.

What are some of the basic properties of a tetrahedron? Quite a few, actually, so I'll stick with a few basic details. Each side of the tetrahedron borders *every other side* of the tetrahedron. This is an unusual property.

They have 4 sides, each of which is a regular triangle. In other words, a tetrahedron consists of four 3-sided sides. There are exactly 12 angles on a tetrahedron. Each of the 4 sides has 3 of the angles, and all angles are identical in their dimensions.

If you want an interesting image running through your head, notice that the shape of a tetrahedron is the basic shape of an archetypal mountain. If you "unfold" a tetrahedron, it unfolds into a triangle with the same basic dimensions as one of the tetrahedron's sides.

Imagine that one deity inhabits each of the 12 interior angles of the tetrahedron, and you can see a bit of a vision of Olympos with the full Dodekatheon in place! Now, isn't that neat?