This sketch (also featured in De Divina Proportione) is da Vinci’s solid edge rendering of the icosahedron. This depiction is called “solid edge” because the faces are see-through and the polyhedron is only viewable in terms of the beams that compose its edges. Notice that in comparison to the solid face approach, it is possible to “see” the backside of the polyhedron— now, one can more easily understand how this polyhedron would occupy three-dimensional space. In a polyhedron as complicated as the icosahedron, it is understandable why da Vinci’s mastery of perspective was crucial in developing a two-dimensional representation of this figure.
Source:
Hart, George W. “Leonardo Da Vinci's Polyhedra.” George Hart, www.georgehart.com/virtual-polyhedra/leonardo.html.
Image Source:
Swetz, Frank J. "Leonardo da Vinci's Geometric Sketches – Icosahedron." Convergence (June 2010), DOI:10.4169/loci002559