Alexandr Korol

a square, and from each of its sides we connect triangles, forming a pyramid. Now imagine another identical pyramid upside down, like a mirror reflection. This rhombus-shaped form, which ends up with eight faces — that’s the octahedron. It’s very important to know this. It’s very important to actually try to build it yourself from sticks — build an octahedron. Then we have the cube — also called by different names, but I call it a cube so that everyone understands. That’s the cube. Next, there is also a geometric figure called the icosahedron. What is the icosahedron? It’s when we look at a cube — not at its flat square face, but at the corner of the cube — then it appears, in perspective, as a kind of hexagon. The icosahedron is also a shape like that — a sort of little sphere made of triangles. It has 20 of these triangles. There’s a band of 10 triangles around the center, then a cap of 5 on top and another 5 on the bottom. Voilà — 20 triangles: that’s an icosahedron. But it’s also important to know how to build it. You can make it out of sticks, and then construct various lines inside to see what shapes form. When I built it, it turned out that each of these geometric elements, each Platonic solid, corresponds to one of the four elements. And the icosahedron represents water — this little spherical form made of triangles, a kind of hexagonal arrangement of triangles, that’s water. And that’s the Spirit of Justice. And if you draw lines from certain vertices within this shape, five-pointed stars — pentacles — appear, which is very interesting. There’s another figure, the dodecahedron. The dodecahedron is somewhat like a soccer ball — not exactly, but close. It has 12 pentagonal faces, and from these 12 pentagons the dodecahedron is formed. These are the geometric shapes: the cube is Earth. The rhombus, or octahedron, is Air. The tetrahedron — those triangles — is Fire. The icosahedron is Water. And the dodecahedron, the ball made of 12 pentagons, is Ether. In the fifth volume, when I begin to comprehend Ether, that corresponds to the dodecahedron... It’s also interesting that when you build an icosahedron and draw various intersecting lines inside it to form pentagrams — pentacles — you end up generating a dodecahedron within the icosahedron. That’s fascinating in terms of how one shape can be inscribed inside another. The dodecahedron, on its own, seems to emerge when I construct the wheels for my cube — for my matrix — and wherever the intersections of the wheel vertices occur, those are the vertices of a dodecahedron, if I were building it on my cube. That’s interesting