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<p>The <i>Divina proportione</i>, first printed in 1509, contains the earliest known graphic representation of the rhombicuboctahedron. Unlike his more detailed treatments of other solid bodies&#xa0;in this book, Luca&#xa0;Pacioli provides only a concise account of how to derive it from the cube, while emphasizing its potential architectural utility. This study reexamines Pacioli’s account to reconstruct the procedure that&#xa0;he may have followed, drawing on textual analysis, Renaissance geometric practice, and comparisons with sixteenth-century mathematicians and artists. Algebraic, geometric, and model-based constructive possibilities are assessed in relation to other procedures discussed in <i>Pars Prima</i>. The paper also discusses the limited reception of the rhombicuboctahedron, evident in a small number of architectural applications.</p>

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Luca Pacioli’s Rhombicuboctahedron: Description, Construction, and Architectural Reception

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Vera Viana

摘要

The Divina proportione, first printed in 1509, contains the earliest known graphic representation of the rhombicuboctahedron. Unlike his more detailed treatments of other solid bodies in this book, Luca Pacioli provides only a concise account of how to derive it from the cube, while emphasizing its potential architectural utility. This study reexamines Pacioli’s account to reconstruct the procedure that he may have followed, drawing on textual analysis, Renaissance geometric practice, and comparisons with sixteenth-century mathematicians and artists. Algebraic, geometric, and model-based constructive possibilities are assessed in relation to other procedures discussed in Pars Prima. The paper also discusses the limited reception of the rhombicuboctahedron, evident in a small number of architectural applications.