I know, it looks like it should qualify - same faces, same dihedral angle and all that. But here is the reason I can think of. In order to be a platonic solid all the angles withing the faces also have to be the same. So in equilateral triangles it's 60, in squares 90, and in the pentagons 108. If you squish a square into a rhumbus the angles change and 2 become acute and 2 obtuse which disqualifies it for the platonic solids club.
Dang, glad I finally got around to watching this one. XD You're doing proofs now! Amazing!
This one was so much fun to make. And I thought it could be helpful to STEM teachers. 3d pens are just such perfect tools for explaining this.
I’m trying to figure out why the Rhombic dodecahedron transforms into the cube but is not part of the Platonic solids.
I know, it looks like it should qualify - same faces, same dihedral angle and all that. But here is the reason I can think of. In order to be a platonic solid all the angles withing the faces also have to be the same. So in equilateral triangles it's 60, in squares 90, and in the pentagons 108. If you squish a square into a rhumbus the angles change and 2 become acute and 2 obtuse which disqualifies it for the platonic solids club.