Reducing a dodecahedron to an equal cube
Twelve pentagonal pyramids resolved into wedges, cylinders and cubes
A dodecahedron of twelve equal pentagonal faces is drawn at the top right, followed by a pentagonal pyramid, the same pyramid with its base split into five triangles, a wedge inside a cylinder, and a triangular prism inside a cylinder. The text (a five-step demonstration keyed to the figures) shows how to turn the twelve-faced solid into a cube: resolve it into 12 pyramids, split each into 5 triangular-based pyramids, reduce each to a wedge, then to a quadrilateral cylinder, and finally assemble the cylinders into a cube of equal quantity. Leonardo remarks that the same could be done with the 60 cylinders from the triangular pyramids, but that route was too long.
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Dodecahedron ('prima') resolved into twelve pyramids
The twelve-faced solid drawn at the top and lettered is the starting body. Leonardo resolves it into 12 pyramids, each of the twelve pentagonal faces becoming the base of a pyramid, then splits one five-sided pyramid into 5 triangular-based pyramids by dividing its pentagonal base into 5 equal triangles.
Pyramid reduced to a wedge and quadrilateral cylinder
The pentagonal pyramid ('seconda'), the same with its base divided in five ('terza'), the wedge inside a cylinder ('quarta') and the prism inside a cylinder ('quinta') show the reduction: one of the five pyramids is brought to the form of a wedge, and from the wedge a quadrilateral cylinder is made.
Assembling a cube equal to the twelve-faced body
Five like cylinders set in one straight line make a cube; twelve such cubes set in a line make a cylinder equal in quantity to the given twelve-faced body, from which the promised cube is finally made. Leonardo adds that the same could be done with 60 of the first cylinders born of the three-sided pyramids, but that it was too long.