Short answer
The Poetry Book is Printed Poetry, made for Gunter during Rhyme and Printed. Complete Congregation Trouble first, then print the quest item and deliver it to the Astrologer at his tower.
The Astrologer's Tower
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Quest and item names
The journal calls it a Poetry Book; the required inventory item is Printed Poetry. Rhyme and Printed follows Congregation Trouble and opens Stars, Lies, & Contracts.
Prepare the Printing Press
The Printing Press belongs in the Writing Basement. Newspaper unlocks its blueprint; building it costs 3 Oiled Beam, 2 Bronze Gear and 6 Iron Detail.
Print the book
The quest unlocks the one-time Printed Poetry recipe: 1 Blank Softcover Notebook, 2 Ink and 1 gold-quality Story. It requires Book writing mastery 4, takes 8 ticks and uses no fuel.
Check the quest unlock, station, mastery and Story quality if the recipe is missing or cannot start. Ordinary notebooks and other books do not replace the quest item.
Deliver it to Gunter
Bring Printed Poetry to Gunter in his tower. The quest awards 10 reputation with him, 1 Town Gratitude, a silver-quality Story and a PR Agreement.
