The building of the Koelner Dom was started in the 13th century and completed only in 1880, the majority of the volume (the nave and the towers) being constructed in the 19th century, but according to original mediaeval plans. You should visit it to appreciate the scale and perspective, a materialization of the celestial Jeruzalem as craftsmen of the middle ages pictured it.
Dependent on how much you're interested in religious architecture, you can spend between an hour and a whole day.
You should definitely try to admire the Trinity Shrine (designed by Nicolas de Verdun) and the 1000-year old crucifix in the choir.
Also recommended is the treasury (Schatzkammer) displaying exquisite objects in precious materials from the early middle ages until the 20th century.
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