Leonardo da Vinci made perspective drawings of solids. Solids can also be represented by planar graphs.
In fact they are very useful to investigate the number of steps to go from a vertex of the solid to the opposite vertex.
Direct connections between vertexes of solids can be represented by a connectivity matrix, which we can multiply.
I started this book reusing the applets with the da Vinci drawings from the GGbook [url=https://ggbm.at/Pr3bvbx3]Graph Theory for kids[/url] by [url=https://www.geogebra.org/voracova]Sarka Voracova[/url]. Starting with these applets I took an investigation of all 5 the Platonic solids and of the 13 Archimedean solids as well.
The next eight archimedean solids grow more and more complex in number of verteces end edges. With up to 120 verteces I won't make connectivity matrices, but I think even just showing the solid and it's planar graph is worthwhile.