Geometry : Interactive network of the convex regular-faced polyhedra

Even though I have not explained anything about convex polyhedra with regular faces yet, I have decided to post this network first. It is a tool I have made to better visualize the construction relationship between the many solids. See also this page [7] for more background about convex polyhedra.

The groups of polyhedra plotted in this graph are: 6 of the Prisms and 5 of the Antiprisms, the 5 Platonic solids [3], the 13+2 Archimedean solids [2], the 92+5 Johnson solids [8, 1] and, finally, the 78+9 convex solids with conditional edges also named Parquethedrons [6]. These groups are represented by different colors. Chiral versions of polyhedra are also represented when they exist.

These convex polyhedra can be separated into two groups: composite and non-composite, see [4, 5]. A composite polyhedra is built from the association (the face to face addition to be precise) of two or more non-composite polyhedra. The label on an arrow indicates which polyhedron to add to the source polyhedron to get the target polyhedron.

Four distinct networks can be observed. Amongst these, one is the legend and one regroups the loners which are non-composite polyhedra which cannot be added to any other solid to form a convex polyhedra.

By hovering over a node, more information about the polyhedron is displayed as well as animations. Details about the creation of these animation are for another post (in a nutshell, I used Blender).

Warning and link

EDIT on 28/08/2022: I have managed to redo the graph with the latest version of visu.js. I have also improved the initialization of the nodes' positions, as well as the loading of the animated pictures. And finally, I made two versions: one (below) with and the other (above) without the physics engine enabled. It should be responding blazing fast now. Hope you enjoy it !
Dynamic Graph

Acknowledgements

I would like to thank David I. McCooey, Robert R Tupelo-Schneck and A.V. Timofeenko for their help. Please go visit their websites or take a look at their work.

References