Jessen's Orthogonal Icosahedron is a concave 20-sided polyhedra that was discovered by Børge Jessen in 1967. It possess a variety of mathematical properties, such as being scissor congruent to a cube and being a "shaky" or multistable shape. Given that there has not been a ton of work on this particular subject, I figured I would design it in CAD and 3D print it to have a physical version.
YouTube Video: https://youtu.be/9-HnJ9n6F20
I covered my results in the video linked above. I found that the shape can undergo a fascinating transformation when made from a flexible material. When compressed, the shape collapses into an octohedron.
Print with 2 shells and .8mm top/bottom thickness in a flexible material such as NinjaFlex or WillowFlex in order to have a collapsible version of the shape