Platonic Solids
Platonic Solids are a set of five, three dimensional, shapes that date back to the Greek mathematician Pythagoras and later named after the Greek Philosopher Plato. The Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron each have unique characteristics, in that the sides, edges and angles are all congruent. In other words, all sides are equal, the angles are the same and the faces are identical.


-- N,E,W,S—being a side of a 4 sided pyramid with a base. Above,below,within ,without—being a side of a 4 sided pyramid with a base. You linked them to a star tetrahedron or merkaba which has only 3 sides and a base.
The merkaba ,3 sides are triangles = trinity=blueprint. Note : the base is also a triangle.
Total---- 4 triangles + 4 triangles = 8 Triangles which total 8 sides.

.The Octahedron is two, 4 sided pyramids--- each with a square base like the great pyramid. -- 4 triangles and 1 square base. Pointing up. 4 triangles and 1 base pointing down. The Octahedron is made up of eight equilateral triangles that are arranged around a single point, with six vertices, eight faces, and twelve edges. Which is formed from placing two square based pyramids base to base.
Total 8 triangles +2 bases = which total 10 sides.

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