The Magazine of the Week is the March 1965 issue of Analog magazine. This issue contains Part III of The Prophet of Dune (really the sixth out of eight installments of the novel Dune). The stunning cover, depicting one of the giant sandworms of Arrakis, is by far the best out of the many cover images John Schoenherr did for Dune, and I am at a loss to explain why it was not used for any of the book editions.
Schoenherr was able to do a large, detailed cover image for Analog because between March 1963 and March 1965, Analog switched from digest to a glossy, oversized (8" x 11") "bedsheet" format. Bedsheet is the most common format for magazines, but is generally not used for science fiction and other literary magazines. This is because bedsheets are expensive to produce, and thus only make sense for magazines that have a large potential audience -- much larger than the small number of us geeks and weirdoes who read science fiction.
With only a few exceptions, bedsheet magazines are the largest-sized items in my collection. Next week's Book of the Week will be one of those exceptions, a book published in a format like a tabloid newspaper. This rare book is sought by collectors of both science fiction and, would you believe, punk rock paraphernalia.