Josep Tarres
I have interests in engineering applied to STEM. Therefore, I am
involved in creating objects that have a geometric background with not
only educational math content but also industrial applications. They
have to be beautiful in order to be appealing to everyone.
The pentachoron (5-cell, 4-simplex) is made of 5 tetrahedron, each
one joined at the other 4 by their faces, 10 triangles (faces), 10
edges, and 5 vertices; the vertex-first projection is a 3D
representation with a vertex at the center. On the other hand,
dissections with polytopes are hardly used. The dissected
pentachoron from above is a proposal of its partitioning in 2
equal polyhedral forms made of 2 tetrahedrons. It has several
features: for instance, all edges are reachable because there are
no inner edges anymore; however, 2 faces are not shown (they are
non-reachable). This mockup might be used as a didactic tool.