Towers of Icosahedra in a Tetrahedron

An icosahedron is placed inside a tetrahedron so that four of their faces are coplanar.
Set the "number of units" to place towers of icosahedra on in the direction of the vertices of with face-to-face connections. The size of each icosahedron is reduced by half relative to the previous one, so the total height of the tower is finite and the tower converges to the vertices of .
Use "show golden lines" to see the golden lines (in blue) of the tetrahedron. (Golden refers to the golden ratio.) The golden lines are extensions of the edges of that lie in the faces of ; only the front three are shown.


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