The tower was assembled in 1934 and 1935 from spare material off the construction of the first Little Belt Bridge — steel that had been ordered for a crossing and ended up pointing straight up instead. It took roughly 30 tons of that steel, 2,700 tons of concrete, and half a million kroner, which in mid-1930s Denmark was a serious sum. It opened on 29 May 1935, inaugurated by Crown Prince Frederik, the future Frederik IX. At 175 metres it immediately became the emblem of Odense and of Funen as a whole. Visitors claimed you could see the entire island from the platforms; if they were right, the horizon was better than fifty kilometres out.

Two platforms carried the public. The lower one held a restaurant built around a great star-shaped room with low, broad windows and seats for 160, and its ceiling was painted as an enormous compass card: a map of Odense at the centre, and radiating out from it the bearing, the name and the coat of arms of every town on Funen. You could sit at dinner and find your own village on the ceiling. Higher up, a second platform opened onto a view that was better still, and a spiral staircase — the reason for the name — wound down to the Conch Bar, where the tables were set one to a step. The kitchen hung beneath the restaurant floor and was considered a marvel of modern engineering. In 1935 alone more than 213,000 people came, many of them foreign, and the open ground below became a favourite launching field for model-aeroplane enthusiasts.

The occupation turned the tower into a target, but not in the way anyone expected. As the Danish resistance stepped up sabotage against German interests in Odense, the response came in the form of Schalburgtage: reprisal destruction of Danish public and cultural property, carried out by Danish collaborators, named after a Danish SS officer. The Odin Tower was demolished by the Peter group under Henning E. Brøndum. It had no military value whatsoever. It was a restaurant with a view — which is precisely what made it worth destroying, since the point of a reprisal is to punish a population rather than an enemy. The tower collapsed completely and was damaged beyond any hope of repair.

Clearing the wreckage took longer than building the thing. The scrap steel was gone in about two months. The 2,700 tons of concrete took almost ten years to break up and cart away, which meant that Odense spent the whole of the immediate postwar period living with the rubble of what it had lost. Nothing was rebuilt in its place. Bolbro Bakke went back to being an ordinary rise on the western edge of Odense, and the tower survived only in photographs of the ruins and in the memory of the people who had eaten dinner under that painted compass.

On 29 May 2004 — the sixty-ninth anniversary of the opening — students from the smithing department of Odense Technical College erected a replica on the original site. It is twelve metres tall, roughly one-fifteenth of the original, which is either a modest tribute or a rather pointed one. A committee has campaigned for years for a full reconstruction, and the argument surfaces in Odense every so often with undiminished energy. In the meantime the small steel tower stands on the hill doing the work a monument does: not replacing what was destroyed, but refusing to let the destruction go unmarked.