CHAPTER XVIII — Critical Commentary & Notes

How Stonemasons and Sculptors Are Highly Commended for Placing the Regular and Dependent Polyhedra in Their Works, and How Phidias Placed the Icosahedron in the Temple of Ceres in Rome.

Historical & Mathematical Commentary

• Architectural Legacy of Pacioli’s Polyhedra: Pacioli's advice in Cap. XVIII to sculptors, stonemasons, and intarsiatori to place the Platonic and Archimedean solids (solid and skeletal) atop capitals, pedestals, finials, and perspective panels had an immediate and lasting impact across Europe:

  • Fra Giovanni da Verona carved Leonardo/Pacioli's skeletal polyhedra into the famous intarsia panels of Santa Maria in Organo in Verona (c. 1519) and Monte Oliveto Maggiore;

  • Wenzel Jamnitzer (Perspectiva Corporum Regularium, Nuremberg, 1568), Lorenz Stoer (Geometria et Perspectiva, 1567), and Jean Cousin placed these exact polyhedra atop classical columns, pedestals, and architectural ruins;

  • Tomb monuments and church finials throughout 16th- and 17th-century Italy (including Hawksmoor’s and Wren’s later obelisks and finials) adopted the regular and stellated polyhedra as crowning architectural ornaments.

• Baron Mario Mellini and the Palazzo della Cancelleria in Rome: Mario Mellini (1456–1503, nephew of Cardinal Giambattista Mellini, resident at the Torre dei Mellini near Piazza Navona, where a famous collection of antiquities and manuscripts was kept) and Cardinal Raffaele Riario / Cardinal Galeotto Franciotti della Rovere at the Palazzo della Cancelleria were Pacioli's hosts in Rome (where Pacioli deposited a fourth set of his polyhedra models!).

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0080 (f. 32v–f. 32v)

• Winterberg 1889 Italian Source: winterberg/02_architectura_italian/018_cap_XVIII.txt

• Winterberg 1889 German Source: winterberg/04_architectura_german/018_cap_XVIII.txt

• Marginal Woodcut Diagrams: 0 figure(s) extracted from the 1509 Venice witness.