DLD Caspar presenting Kepler's solar system
in Dürer's pentagonally illuminated sanctum

Computer graphics construction by Jim Clarage on the occasion of Don Caspar's 70th birthday, January 8, 1997. Using Photoshop, Clarage has revised the photograph by Marie Craig to show Caspar holding the 1597 engraving of Johannes Kepler's Platonic model of the solar system from his Mysterium Cosmigraphicum. Clarage superimposed this image on Albrecht Dürer's engraving of St. Jerome, in which he replaced the glazing and shadows of the foremost stained glass windows with projections from a pentagonal lattice illustrated in the paper on Five-fold Symmetry in Crystalline Quasicrystal Lattices by Caspar and Eric Fontano (Proc. Natl. Acad. Sci. USA 93, 14271-14278, Dec. 1996). This pentiling pattern superposes an extension of Kepler's pentagonal tiling from his Harmonices Mundi (1619) on Roger Penrose's first quasiperiodic pentagonal tiling from his Pentaplexity article (Math. Inteligencer 2, 32-37, 1979); these tilings are each arranged with the five-fold symmetry of Dürer's basic pentagonal packing illustrated in his Manual of Measurement of Lines, Areas and Solids (1525). Clarage's frame pattern for his montage is an elliptically distorted version of the autocorrelation function of Caspar and Fontano's pentiling lattice.