Here is the collection of 7 cones for the tetrahedra on its own (the cones themselves are infinite, but we draw them as finite square or triangular pyramids.)
Omar says Benoît Bertrand and Lucía López de Medrano don’t believe this is a new result, but they have not been able to find a reference to it.
https://mathstodon.xyz/@oantolin/116656345048312313
