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Re: [sacredlandscapelist] Roman Dodecahedrons

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  • mikebispham@cs.com
    From http://math.truman.edu/~thammond/history/RegularSolids.html Emmer, Michele. Art and mathematics: the Platonic solids. The Visual Mind, 215--220, Leonardo
    Message 1 of 1 , Jun 3, 2000
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      From http://math.truman.edu/~thammond/history/RegularSolids.html

      "Emmer, Michele. Art and mathematics: the Platonic solids. The Visual Mind,
      215--220, Leonardo Book Series, MIT Press, Cambridge, Mass., 1993.

      The author begins by mentioning some ancient representations of Platonic
      solids. These include a pair of Egyptian die from the Ptolemaic dynasty, an
      Etruscan dodecahedron (at least 2500 years old), two Celtic dodecahedra, and
      a West German dodecahedron from the 2nd century BC. The author continues with
      a discussion of the regular solids in Plato's Timaeus. The author notes that
      Dürer's Melancholia, which includes a truncated rhombohedron, is sometimes
      thought to show the influence of Luca Pacioli. The magic square in the
      painting gives some evidence for this; Dürer's engraving may be one of the
      earliest depictions of a magic squares in the West, but an earlier manuscript
      by Pacioli showed an interest in them. On the other hand, Luca Pacioli's De
      Divina Proportione relied heavily on, and perhaps even appropriated the work
      of Piero della Francesca. The book is also notable for its pictures of the
      regular solids, attributed to Leonardo da Vinci. Also discusses work on the
      regular solids due to Johannes Kepler, including Kepler's recognition of a
      duality and his idea of a combination of two tetrahedra called a stella
      octangula. The author notes that the notion of the stella octangula also
      appears in Pacioli's De Divina Proportione. In addition, Kepler's stellated
      dodecahedron occurs in mosaics in the San Macro Cathedral in Venice; this
      work is thought to have been done by Paolo Uccello. "

      Mike

      Roland wrote:
      Hi List,

      This is a very interesting site. It features Roman Dodecahedrons that have
      been unearthed, there use is still a mystery.

      http://www.cpu.lu/gka/d_bgr/d_bgr.htm

      RM
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