By Swami Chinmayananda (Balakrishna Menon)
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Vasari's inconsistency in saying where to look was derided, and his many other errors in matters of fact were called to witness how unreliable he was. What did an artist like Vasari know about mathematics anyway? Someone in Piero's family must have planted this exaggerated story, which the credulous Vasari accepted. Defenders of Pacioli pointed out that Pacioli, so far from being an enemy, lauds Piero highly, calling him Monarca della Pittura, an epithet which has stuck. ) As late as 1911 the Encyclopedia Britannica dismisses Vasari's allegation on grounds like these.
Cromwell, "Kepler's Work on Polyhedra", The Mathematical Intelligencer Vol. 17, No. 3, New York (1995), 23-33.  Nicolo Tartaglia, Trattato Generale di Numeri e Misure, Venice (1559).  Nicolo Tartaglia, op. , Part IV Book 2, and Part V Book 2.  Nicolo Tartaglia, op. , Part I Book 13, fol. 107r.  In this paragraph I paraphrase arguments culled from 18th century sources by Gino Arrighi and quoted by him in the introduction to Ref. . Note added i n proof: Proceedings of a 1992 conference held in Arezzo and Sansepolcro appeared after this work was done.
It is correct, o f course. The Archimedean Solids It h a s long b e e n recognized t h a t Piero r e d i s c o v e r e d 6 of the 13 A r c h i m e d e a n solids , . He did n o t think in t e r m s o f a c o m p l e t e classification, b u t simply o b t a i n e d n e w s e m i r e g u l a r p o l y h e d r a b y t r u n c a t i n g e a c h regular polyhed r o n at the vertices. The r e a s o n he found 6 A r c h i m e d e a n solids i n s t e a d of 5 is that t h e r e is m o r e than one w a y to truncate, and in going from the Trattato to the Libellus he s u b s t i t u t e d one n e w one.
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