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I'm currently studying polytopes and using the book Lectures in Geometric Combinatorics by Thomas. When I come to Schlegel diagrams, I do not quite understand how to determine whether a Schlegel diagram is a Schlegel diagram. In the book on p. 34, it states that if $\mathcal{D}$ is indeed a Schlegel diagram, then $\mathcal{D}$ is a regular subdivision of $|\mathcal{D}|$, the support of $\mathcal{D}$. Can anyone help me with this?

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    Ed pegs description is good and complex2014-06-09

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Page 34 of "Lectures in Geometric Combinatorics" gives a diagram of a non-Schegel diagram. Not a very intuitive description, is it? You'll likely find the following explanation more useful:

Definition of regular subdivisions