Pentakis Dodecahedron Puzzle

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The sixty triangular faces of a Pentakis Dodecahedron can be arranged in numerous configurations, each consisting of isosceles triangles. At each side of these triangles, four possible positions are available: right from the center (R), far right from the center (RR), left from the center (L), or far left from the center (LL). With gaps created at the chosen positions, a total of 64 different triangular configurations can be achieved. If pieces with identical chosen positions on each side are eliminated, exactly sixty pieces remain, which is just enough to construct the Pentakis Dodecahedron by matching edges where L meets R and LL connects RR.