Solid Objects: 16th-Century Geometric and Perspective Drawings

This sequence of increasingly complex geometrical figures and perspective drawings — collected in a sixteenth-century watercolor manuscript and preserved at the Herzog August Bibliothek in Wolfenbüttel — comes with no author's note, editor's preface, or running commentary. We know very little about its origins. All we have are shapes and color, with the occasional totem (eagle, rooster, and even a putto holding something like a pinwheel) dwarfed by the immensity of lines and angles. 

When compared to other geometric images contemporary to the manuscript, it inhabits a middle ground between the sober studies found in Augustin Hirschovogel's Geometria (1543) and Lorenz Stoer's ethereal geometric landscapes (1567). While the manuscript remains a mystery, certain pages share a strong resemblance to the etchings by Jost Amman for Nuremberg goldsmith Wenzel Jamnitzer's Perspectiva corporum regularium (1568) — and one image bears the inscription "Geometria et Perspectiva Corporum Regularium" (Geometry and Perspective of the Regular Bodies), though this was a somewhat common descriptive name for studies of this kind.

Indeed, the manuscript displays the German Renaissance fascination for geometrical solids demonstrated by Jamnitzer, Albrecht Dürer, Johannes Kepler, and Hans Lencker, which paralleled similar experiments in Italy conducted by Piero della Francesca, Paolo Uccello, Leonardo da Vinci, and several others — part of a larger "rise of perspective" in visual art and the renewed mathematical fascination with polyhedra. According to Thomas Christensen, it was thought that one could derive, from geometric solids, "God's secret design for the universe". 

Without a precis or introduction, we might find ourselves adrift in a world of forms, were it not for the intuitive logic exhibited in the order of these drawings. After the pyramid and cube, we find an icosahedron — a polyhedron with twenty sides, the progressive extrapolation of those earlier shapes. Then a beautiful, ruby-painted variation of the "great dodecahedron", which contains pentagrams in its excavations. And suddenly, compounds: combinations of octahedrons and cubes, faceted and almost stellated in certain instances. 

As the geometry becomes more complex, the drawings gain worldly details: a spherical surface covered with a triangular mesh is staged on an angular stand, the kind that you might find attached to a globe, situating the abstract realm of mathematical possibility against solid ground. A beautiful example in this regard features a pale-yellow sphere, which has been grooved like a paper lantern or an ornamentally peeled orange. It sits on an irregular jade barrel, stacked on a low pink table. The tower of shapes leans slightly rightwards, lending a profound sense of movement to the otherwise meaningless collection of surfaces. On the left, leg raised, a white wagtail sounds its approving chisick

The concluding pages create a grand finale: lattice spheres; elongated pastel pyramids that resemble someone's dream of an ancient city; two tori, cut, interlinked, and set upon a pedestal, like a surrealist sculpture of donuts hugging; a very unexpected and realistic lute, floating over a lily-padded toad; and then, the manuscript's penultimate perspective drawing — a carmine book, whose cover is inscribed with an abstract shape, opened to show a cross resting on a stand. At this point in the series, steeped in curves and surfaces, the singular Christian symbol summons a sense of geometry both profane and sacred: although many are utterly commonplace, the forms in this manuscript seem to transport us just beyond the realm of comprehension.

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