The present article discusses a Raphael drawing in the form of a chiaroscuro woodcut depicting Archimedes Contemplating an Icosahexahedron and offers a rare insight into Raphael's visual planning for one of his canonical works, the School of Athens. Preliminary ideas are known for two other frescoes in the Stanza della Segnatura: a drawing for the Disputà, and Marcantonio's engraving for the Parnassus. The present author submits a preliminary disegno for a figure in the third fresco, which suggests an earlier and other meaning for the School of Athens. Raphael, clearly the image's designer, always drew for work underway. The article asks several questions on a subject of an image of an ancient philosopher contemplating an icosahexahedron with faces mis-shapen from the square.

Part A
What was the subject's destination? Given the c. 1510 date of the drawing, it must have been prepared for the School of Athens of the Stanza della Segnatura. — How did Raphael know that Archimedes had invented the icosahexahedron? And from where did Raphael get the polyhedron's form? Answering the question involves examining Luca Pacioli's method in arriving independently at that polyhedron, pictured in Divina proportione. — Why was the polyhedron mis-shapen when the Divina's plate shows congruent planes? The mis-shapen form put Archimedes in dialogue with Bramante/Euclid by encoding the crossing of St Peter's. Pacioli was unaware of Archimedes's prior discovery. The article traces the geometric means by which he arrived at the body anew, in order to account for its textual position. The non-corresponding position of the plate is, instead, linked to another body that Pacioli, who was architecturally therefore spatially aware, could have adjusted to its true form. — Why was Archimedes expunged? He vitiated the power of Euclid, the historical personification of geometry. In Aristotle's realm, it was Euclid, of these two geometers, who fulfilled the prescription of higher purpose, that of theoretical wisdom. Raphael then transferred the encoded tribute to Bramante from the icosahexahedron to a diagram on the Bramante/Euclid tablet that indicates Bramante's design of the painted space of the School of Athens.
Raphael's preliminary thoughts, preserved in drawings for the Stanza della Segnatura, are very rare. The present article is the first to identify the early purpose of this design, and to recognize the figure's later manifestation as St. Andrew in the Transfiguration.

Part B
Of the chiaroscuro woodcut itself, only two impressions are known. Of the genre, it is the sole example in which Leonardo's dark manner is engaged. Because of the print's technical importance, the present author has traced the evolution of Ugo Panico da Carpi's graphic skill in the context of Leonardo's influential painterly mode in the Transfiguration and in Parmigianino's Vision of St. Jerome.