Constructing the Cubus simus and the Dodecaedron simum via paper folding
Urs Hartl, Klaudia Kwickert
TL;DR
This paper presents explicit paper folding constructions for the Archimedean solids Cubus simus and Dodecaedron simum, which cannot be built with ruler and compass, highlighting the elegance of the folding method for the snub cube.
Contribution
It introduces explicit paper folding constructions for the snub cube and snub dodecahedron, expanding geometric construction methods beyond classical ruler and compass techniques.
Findings
Folding constructions for Cubus simus and Dodecaedron simum
Review and proof of construction rules for other Archimedean solids
Demonstration of the elegance of folding methods for complex polyhedra
Abstract
The archimedean solids Cubus simus (snub cube) and Dodecaedron simum (snub dodecahedron) cannot be constructed by ruler and compass. We explain that for general reasons their vertices can be constructed via paper folding on the faces of a cube, respectively dodecahedron, and we present explicit folding constructions. The construction of the Cubus simus is particularly elegant. We also review and prove the construction rules of the other Archimedean solids.
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