Here I have the following definitions for Schlegel diagram and d-diagram.
I don't understand the last two examples at the end of the latter definition.
For this one,
how do we know that it's not a Schlegel diagram?
And for this one,
why isn't it a d-diagram?
From the first pic you'd deduce that the second pic ought be a triangle prism with diagonals drawn onto the squares, or at least some parallely truncated triangular pyramid with diagonals drawn on the tetragons. But surely such additional edges would ask to be inserted between 2 coplanar faces, which is not allowed for convex polyhedra.
The third pic cannot be a polyhedron either, as there would be 3 vertices (e.g. the bottom one of that pic), which would have just 2 incident faces.
--- rk