Dimensions
If the edge length of a rhombic triacontahedron is a, the radius of a inscribed sphere (tangent to each of the rhombic triacontahedron's faces) is:
where φ is the golden ratio.
The plane of each face is perpendicular to the center of the rhombic triacontahedron, and is located at the same distance (short diagonals belong only to the edges of the inscribed regular dodecahedron, while long diagonals are included only in edges of the inscribed icosahedron). Using one of the three orthogonal golden rectangles drawn into the inscribed icosahedron we can easily deduce the distance between the center of the solid and the center of its rhombic face.
Read more about this topic: Rhombic Triacontahedron
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—Thomas Jefferson (1743–1826)
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—Henry David Thoreau (1817–1862)