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Wenninger published his book Polyhedron models, which lists all 75 nonprismatic uniform polyhedra, with many previously unpublished names given to them by Norman Johnson.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 our era is the nauseating and repulsive history of the crucifixion of the procreative body for the glorification of the spirit.”
—D.H. (David Herbert)
“When the coherence of the parts of a stone, or even that composition of parts which renders it extended; when these familiar objects, I say, are so inexplicable, and contain circumstances so repugnant and contradictory; with what assurance can we decide concerning the origin of worlds, or trace their history from eternity to eternity?”
—David Hume (1711–1776)
“No cause is left but the most ancient of all, the one, in fact, that from the beginning of our history has determined the very existence of politics, the cause of freedom versus tyranny.”
—Hannah Arendt (1906–1975)