In architecture Durer cites Vitruvius but elaborates his own classical designs and columns. In typography, Durer depicts the geometric construction of the Latin alphabet, relying on Italian precedent. However, his construction of the Gothic alphabet is based upon an entirely different modular system. The fourth book completes the progression of the first and second by moving to three-dimensional forms and the construction of polyhedra. Here Durer discusses the five Platonic solids, as well as seven Archimedean semi-regular solids, as well as several of his own invention. In all these, Durer shows the objects as nets. Finally, Durer discusses the Delian Problem and moves on to the 'construzione legittima', a method of depicting a cube in two dimensions through linear perspective. It was in Bologna that Durer was taught (possibly by Luca Pacioli or Bramante) the principles of linear perspective, and evidently became familiar with the 'costruzione legittima' in a written description of these principles found only, at this time, in the unpublished treatise of Piero della Francesca. He was also familiar with the 'abbreviated construction' as described by Alberti and the geometrical construction of shadows, a technique of Leonardo da Vinci. Although Durer made no innovations in these areas, he is notable as the first Northern European to treat matters of visual representation in a scientific way, and with understanding of Euclidean principles. In addition to these geometrical constructions, Durer discusses in this last book of Underweysung der Messung an assortment of mechanisms for drawing in perspective from models and provides woodcut illustrations of these methods that are often reproduced in discussions of perspective. 
What kind of solids does Durer discuss in his fourth book?
Seven Archimedean semi-regular Solids