How do I prove this is geometrically impossible?

No.12026666 ViewReplyOriginalReport
Hey there.
I was having a chat with some friends about this image that's going around in the internet.
You know the drill: social distancing guidelines.
At first glance it's clearly wrong, but one of my friends said very cleverly "What if they're not on the same plane?".
I can see how it actually would work if only one of the "diagonals" had to be 1.5m, and I'm quite sure it's impossible with both of them being there.
I have no idea on how to prove it, tho. I thought about using the x,y,z coordinates of each point and the point-distance formula (sqrt(dx2 + dy2 + dz2)) to create a 6-equation linear system in which all distances equal 1.5m; That doesn't seem very elegant tho.

Does anyone have a better idea?