# Reference needed for lower bound on number of guards in three-dimensional art gallery guarding

During my research (writing my master's thesis) I've stumbled across the book Art Gallery Theorems and Algorithms by O’Rourke. In chapter 10 (pdf available on the above site), section 10.2.2. he shows a lower bound of $\Omega\left(n^{3/2}\right)$ on the number of guards needed in three-dimensional art gallery guarding. He says (bold marking is by myself):

In fact, we describe in this section a polyhedron constructed by Seidel that has these two properties.

I believe that the construction, as presented in the book, is not fully correct and thus I tried to find the original work by Seidel. Sadly there is no reference in this section and the only reference in the book with Seidel is Constructing Arrangements of Lines and Hyperplanes with Applications by H. Edelsbrunner, J. O’Rourke, and R. Seidel which does not include the construction.

I have looked through Seidels Google Scholar page but there seems to be nothing relevant.

In one of his papers, Seidel even refers to O'Rourke's book for a description of his own construction. He writes on top of page 253 of his joint paper with Jim Ruppert: "In his book [9, p. 255] O'Rourke describes n-vertex three-dimensional polyhedra that require $\Omega(n^{3/2})$ guards."