Art

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The Renaissance artists e.g. Pierro della Francesca  ( 1 , 2 ) ,Lorenz Stör (1, , 3 )Ucello, Hans Hayden ,,Lorenz Zicken, Jean Cousin (id.) Wenzeln Jamnitzer, Luca Pacioli , Leonardo da Vinci used the Greek geometry in their paintings and sculptures. Battista Alberti (1404-1472) described in Della Pittura  for the first time the mathematical construction of the perspective with a “centric point”. The first three-diemensional figures to appear were the regular polyhedra , often made in the form of intarsia (wood inlay) by intarsiatori . Giovanni da Verona  is one of the most famous.

   Dürer designed his own polyhedron in his etching Melancholia.( http://www.artglobe.se/Ghist/ghist_06.htm A lead copy of this polyhedron was exhibited by the UK sculptor Antony Gormley in 1989.

 In modern art polyhedra occur in pictures and sculptures, e.g. in Dali´s The Sacrament of The Last Supper (takes place in a dodecahedron), (alt), http://ellensplace.net/dali.html  Dodecahedra also occur in Dali´s Searching for the Fourth Dimension ( 1979),  in Rock and Infuriated Horse Sleeping under the See (1947) ,  in Pentagonale Sardana (1979) and in some illustrations in Esseys of Michel de Montaigne.

 Several Russian artists, Malevitch and Rodtjenko were familiar with polyhedron and polygon structures (c. 1920 -1930).

 M. C. Escher often used polyhedra in his etchings, e.g. the dodecahedron and the small stellated dodecahedron. Stars, wood engraving 1948, stellated polyhedron.

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Goethe brought an ancient sculpture from Italy.
Islamic art is often geometric.
A Belgian note with platonic solids
The Golden triangle in a pentagon.

Even today several artists construct polygons and platonic bodies (alt))as well as Archimedean polyhedra ,e.g.
Collection of Dodecahedra
K G Nilson : Red Score
Pål Svensson Platonic solids
Per Svensson:  Platonic solids and Truncated icosahedron (id..)
Lennart Mörk: Platonic solids

Rolf Wilhelmson: Dodecahedron
Legotype of Bauhaus

In architecture, particularly in the USA, polyhedra occur in constructions.