A nice little three-liner: http://gosper.org/johnson7.pdf . Is it convex? This pdf is a spoiler for a programming lab (https://lab.open.wolframcloud.com/app/) notebook because I have yet to figure out how to unrestrict public access. But wouldn't it be a great way for math-funsters to share typesetting, images, animations, and interactions?
If not convex, exactly what is that nearly straight angle? Note that evil (and misnamed) FindGeometricTransform coerces to floating point!
[Mathematica developers: Needs Exact->True option. MachinePrecision isn't quite sufficient
for RootApproximant to reconstruct the algebraics here. A consolation would be WorkingPrecision.]
]
I think at some point I exhaustively searched PolyhedronData for Johnson glue jobs and found even narrower convexity failures. Johnson was working with cardboard? —rwg I need to tweak gosper.org/johnsonposter.pdf to disambiguate some hidden undersides.