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[Alexandr Korol]

together to create some figure. For example, I made a bunch of tetrahedrons, glued them together, and formed an octahedron; glued those together and formed a Merkaba; glued those together and formed a cube. You can also glue many tetrahedrons together to create an icosahedron or a dodecahedron. And the system keeps guiding me to see all the ways to construct triangles in these matrices: inside or outside, with triangles pointing inward or outward, built from different edges or vertices, how different they are, and so on. The last method I tried yesterday was very interesting, but — imagine — it didn’t quite fit, though maybe it just hasn’t fit yet. Here’s the idea: imagine the icosahedron — a sphere made of 20 triangles. Inside this sphere, you can draw lines so that a dodecahedron forms inside as the core of the icosahedron. Now, here’s the next part. To this dodecahedron inside the icosahedron, the dodecahedron has edges and vertices, and on those vertices, you can actually form tetrahedrons pointing outward, like spikes on a hedgehog on the dodecahedron. So you can grow tetrahedrons on it with correct construction, and all these tetrahedrons from the dodecahedron inside the icosahedron start to beautifully protrude from the centers of the icosahedron’s triangles. That means on each face of the icosahedron, a beam from the dodecahedron sticks out. Imagine that. And it all fits beautifully. I hypothesized that since the icosahedron’s faces are triangles, if you make those triangles point inward, they fit into the triangles sticking out from the dodecahedron, pointing outward, and that forms the Merkaba — a sphere of Merkabas, and therefore of cubes. And there you have it: icosahedron, dodecahedron — all of it. I was stunned, wow, I’ve solved it all.
Then I realized, no, it can’t be that simple, and it turned out it didn’t quite fit. But why have I been struggling lately with the icosahedron and the dodecahedron? Because they have so much in common — they seem like reflections or continuations of each other; they are very closely connected. Why? Because the dodecahedron has 12 faces, and the icosahedron has 12 vertices. You see? But here’s the twist: the icosahedron has 20 faces, and the dodecahedron has 20 vertices. You’re probably getting confused. But all of this definitely needs to be shown schematically. But the point is, let’s look at it differently. You understand that a soccer ball,