History
- The Platonic solids date back to the classical Greeks and were studied by Plato, Theaetetus and Euclid.
- Johannes Kepler (1571–1630) was the first to publish the complete list of Archimedean solids after the original work of Archimedes was lost.
Regular star polyhedra:
- Kepler (1619) discovered two of the regular Kepler–Poinsot polyhedra and Louis Poinsot (1809) discovered the other two.
Other 53 nonregular star polyhedra:
- Of the remaining 53, Albert Badoureau (1881) discovered 36. Edmund Hess (1878) discovered 2 more and Pitsch (1881) independently discovered 18, of which 15 had not previously been discovered.
- The geometer H.S.M. Coxeter discovered the remaining twelve in collaboration with J. C. P. Miller (1930–1932) but did not publish. M.S. and H.C. Longuet-Higgins and independently discovered 11 of these.
- Coxeter, Longuet-Higgins & Miller (1954) published the list of uniform polyhedra.
- Sopov (1970) proved their conjecture that the list was complete.
- In 1974, Magnus Wenninger published his book Polyhedron models, which lists all 75 nonprismatic uniform polyhedra, with many previously unpublished names given to them by Norman Johnson.
- Skilling (1975) independently proved the completeness, and showed that if the definition of uniform polyhedron is relaxed to allow edges to coincide then there is just one extra possibility.
- In 1993, Zvi Har'El produced a complete kaleidoscopic construction of the uniform polyhedra and duals with a computer program called Kaleido, and summarized in a paper Uniform Solution for Uniform Polyhedra, counting figures 1-80.
- Also in 1993, R. Mäder ported this Kaleido solution to Mathematica with a slightly different indexing system.
- In 2002 Peter W. Messer discovered a minimal set of closed-form expressions for determining the main combinatorial and metrical quantities of any uniform polyhedron (and its dual) given only its Wythoff symbol.
Read more about this topic: Uniform Polyhedra
Famous quotes containing the word history:
“The history of every country begins in the heart of a man or a woman.”
—Willa Cather (1876–1947)
“There is nothing truer than myth: history, in its attempt to “realize” myth, distorts it, stops halfway; when history claims to have “succeeded” this is nothing but humbug and mystification. Everything we dream is “realizable.” Reality does not have to be: it is simply what it is.”
—Eugène Ionesco (b. 1912)
“The history is always the same the product is always different and the history interests more than the product. More, that is, more. Yes. But if the product was not different the history which is the same would not be more interesting.”
—Gertrude Stein (1874–1946)