That shivery Soviet pleasure is now a thing of the past. The pool has been drained. In its place, the city is to build a carbon copy of the Cathedral of Christ the Saviour, which stood here from the 1880s until 1931, when Stalin's men knocked it down.
Rebuilding the cathedral, which accommodated 10,000 people, will take three years and cost around pounds 150m; Leonid Vavakin, Moscow's chief architect, says the money is being raised entirely by private donations. In a nod to the rise of the ultra-capitalist new rich, a huge underground car-park has been incorporated into the plans. In a nod to the increasingly powerful right-wing Slav nationalists, control of the artwork inside the cathedral has been given to Ilya Glazunov, an Orthodox painter who espouses the return of the monarchy.
The site of the swimming- pool cathedral, a backwater of Moscow marshland, has no obvious charms, yet for two centuries unlimited amounts of autocratic passion, energy and money have been poured into it. Tsar Alexander I ordered a cathedral to be built here to thank God for Napoleon's defeat in 1812.
By the time work started 20 years later, the reactionary Slavophile Nicholas I was on the throne. When complete, the cathedral, designed by Konstantin Thon, was a Slavic overdose of onion domes and Orthodox icons. It sent shivers down the spines of Moscow's intelligentsia, who thought it kitsch. To the Bolsheviks, it represented everything they hated most about Tsarism.
In 1931, an international competition was held for the design of a giant Palace of Soviets to be built on the site, a building, said Stalin, 'our enemies could not even dream of'.
Hundreds of designs were submitted by avant-garde architects and artists, Le Corbusier, Naum Gabo, Auguste and Gustave Perret, Erich Mendelsohn, Walter Gropius and Hannes Meyer among them.
Boris Iofan, a Russian, won. His round, tapering building was to be 720ft high. Not enough for Stalin. Aware that the Eiffel Tower was 980ft and the Empire State Building 1,245ft, he decreed the Palace of Soviets should be stretched to 1,375ft and topped with a 230ft statue of Lenin.
Work began in 1939, but was abandoned when Hitler invaded the Soviet Union in 1941. Meanwhile, the cathedral had been stripped of its cupolas, its treasures were scattered, melted down or stolen, and the hundreds of tons of marble cladding its walls dragged underground to build Kropotkinskaya metro station. When it was finally blown up, a cloud of dust hung over Moscow for days.
Now history has come full circle and Alexei II, the Russian patriarch, is to rebuild the cathedral on the foundations laid for the Palace of Soviets. A third of the church's treasures have been traced and plans are afoot to get them back. Even the altar, now in the Vatican, is to be returned.
A recent convert to orthodoxy, Leonid Vavakin says that plans for the revived cathedral are surrounded in superstitious fears. One legend has it that the site was cursed by the abbess of the nunnery demolished to make way for Nicholas I's cathedral. To break the curse, a replacement Alexeyevsky nunnery is to be built beside the new cathedral.
The old cathedral, it is said, exercised a malign influence on the nearby Kremlin in the past, and might do so again when rebuilt. 'The skyscrapers built this century will shield the Kremlin from any bad vibes,' says the architect blithely.
Nostalgia for a past that might have been, if there had never been a Soviet Union, is widespread in Russia. It is a longing that has been hijacked by the extreme right - the Black Hundreds, monarchists, anti-Semites, fascists and freelance mercenaries fighting with the Bosnian Serbs - who voted for Vladimir Zhirinovsky in last December's election, winning him 24 per cent of the vote.
Mr Vavakin, however, says that rather than a rallying point for right-wing extremists, the cathedral 'will be a symbol of repentance, of atonement for all the sins committed on Russian soil in the last 70 years'. Mr Glazunov, the nationalist painter, goes further. He wants to see Russia regain not only its Christian faith but also its imperial muscle. Rebuilding the church, he says, help.
The artist's latest exhibition, showing lurid canvases of warriors, kings and priests has attracted queues of visitors including Mr Zhirinovsky. And, to the horror of liberals, the once- radical president, Boris Yeltsin, spent a much-publicised hour praising Glazunov's Russian anthems.
'I hope the church will be a symbol of the rebirth of Russia,' says Mr Glazunov from his museum-like Moscow apartment, surrounded by gold-encrusted icons and antique portraits of the Tsars. 'That rebirth is our reason for living. There are many forces, international and internal, which don't want that rebirth; none of them want to see the Russian bear become mighty again. But,' he says, looking at plans of the new cathedral, 'everything is in God's hands.'
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