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All typos and mistakes are corrected in the pdf version. Some were corrected in the second printing of the hardcover. Pages 25/26: For those readers interested in a self-contained proof of the equivalence of vertex and hyperplane description of a polytope, the second printing (and the pdf version) contains a new appendix. Pages 36/37: With our definition of BiPyr, Theorem 2.6 holds only if Q contains the origin. Page 79, Exercise 3.12: Delta(d,1) and Delta(d,d-1) are not equal (though they are both regular simplices). Page 91, Open Problem 4.14 has been solved by Christian Haase, Benjamin Nill, and Sam Payne. Page 157, second paragraph: "vector space" needs to be replaced by "Z-module." The same applies to the hint for Exercise 3.13 on page 206. Page 180 & 182, Examples 11.1 & 11.3: each of the cos-1(1/sqrt(3)) is missing a factor of 1/(2 pi). Page 190, Open Problem 11.14 has been solved by Steven Sam. Page 208, hint for Exercise 9.2: the big union in the sixth line should be a big intersection. The links to the math biographies at St. Andrews have unfortunately changed. "Biographies/" needs to be replaced by "Mathematicians/".
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"The world is continuous, but the mind is discrete."
David Mumford