Final Stellation of The Icosahedron - History

History

• 1619: In Harmonices Mundi, Johannes Kepler first applied the stellation process, recognizing the small stellated dodecahedron and great stellated dodecahedron as regular polyhedra.
• 1809: Louis Poinsot rediscovered Kepler's polyhedra and two more, the great icosahedron and great dodecahedron as regular star polyhedra, now called the Kepler–Poinsot polyhedra.
• 1812: Augustin-Louis Cauchy made a further enumeration of star polyhedra, proving there are only 4 regular star polyhedra.

• 1900: Max Brückner extended the stellation theory beyond regular forms, and identified ten stellations of the icosahedron, including the complete stellation.
• 1924: A.H. Wheeler in 1924 published a list of 20 stellation forms (22 including reflective copies), also including the complete stellation.
• 1938: In their 1938 book The Fifty Nine Icosahedra, H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie stated a set of stellation rules for the regular icosahedron and gave a systematic enumeration of the fifty-nine stellations which conform to those rules. The complete stellation is referenced as the eighth in the book.
• 1974: In Wenninger's 1974 book Polyhedron Models, the final stellation of the icosahedron is included as the 17th model of stellated icosahedra with index number W₄₂.
• 1995: Andrew Hume named it in his Netlib polyhedral database as the echidnahedron (the echidna, or spiny anteater, is a small mammal that is covered with coarse hair and spines).