I understand the argument some people are making as "my intuition tells me it's impossible because $X" and that makes sense. My intuition tells me that there's

I understand the argument some people are making as "my intuition tells me it's impossible because $X" and that makes sense. My intuition tells me that there's an extra node not pictured, let's call it Z. There's a triangle ADZ that's out of view and a planar surface DZCF that mirrors DABE. I'm sure my intuition is wrong too, but without pulling out some kind of CAD I can't really see why.