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Capture the three Golems in Ruby, Sapphire, or Emerald. Migrate the three Golems from Ruby, Sapphire, or Emerald. Visit Pal Park in Platinum. Start the Catching Show in Pal Park. Walk through the grass in Pal Park until you encounter your first Pokemon. Throw a Park Ball to instantly capture the Pokemon. Make sure all three Golems are in your party. Head to Snowpoint Temple. Get to the bottom of the temple. Save the game before starting the battle. Start the battle with Regigigas. Use False Swipe to carefully lower Regigigas' health. Paralyze Regigigas or put it to sleep. Throw Heavy Balls or Level Balls to capture Regigigas.
The only way to get Regigigas in Platinum is to have the three Golems (Regice, Regirock, and Registeel). These cannot be caught in Platinum without a special event Regigigas, so you'll need to transfer the three Golems from Emerald, Ruby, or Sapphire, where they're much easier to obtain. See Catch the 3 Regis in Pokémon Sapphire or Ruby for instructions on getting the three Golems.  There are essentially two scenarios for obtaining the three Golems and Regigigas in Platinum. The common way is to transfer the three Golems from Ruby, Sapphire, or Emerald, then capture Regigigas in Platinum. The other way involves using a special event Regigigas in Platinum to obtain the three Golems without Ruby, Sapphire, or Emerald. Since the event is over, this is no longer possible without cheating. If you don't have access to Ruby, Sapphire, or Emerald, see the next section for cheating instructions. This is the only other way to get all three Golems and Regigigas in Platinum. Once you have the three Golems in your Ruby, Sapphire, or Emerald game, you can transfer them to your Platinum game. This will allow you to find the Regigigas in Platinum, which only becomes available when you have the three Golems.  You'll need to have completed the National Pokedex in Platinum to access Pal Park. This means seeing every Sinnoh-region Pokemon. Insert your Ruby, Sapphire, or Emerald cartridge in the GBA slot of the DS system, then start Platinum and select "Migrate from Pokemon Ruby/Sapphire/Emerald." Select the six Pokémon you want to transfer, including the three Golems. You must select exactly six Pokémon when using Pal Park to move Pokémon from one game to the other. You'll find the Pal Park facility off Route 221. You can get there the quickest by flying to Sandgem Town, surfing to Route 219, going south to Route 220, then northeast to 221. You'll need to talk to the person at the front counter to start it. You'll need to have completed your Sinnoh National Pokedex to start the Catching Show. You'll only encounter the six Pokémon that you transferred earlier. Each Park Ball will capture the Pokémon you encounter. Repeat this until you've captured all six Pokémon that you transferred, including the three Golems. You'll need all three in your active party in order to get Regigigas. You'll find the entrance to this temple in Snowpoint City. Like Pal Park, you'll need to have completed the National Pokedex in order to enter the temple. You'll need to get down to B5F, which is the sixth floor of the temple. You'll encounter a lot of Rock Pokémon with levels ranging from 47-56. You only get one chance at Regigigas, so you'll want to save before the battle just in case. This will allow you to restart if you accidentally knock it out. Regigigas will only be level 1, so make sure you don't attack it with anything that will knock it out. Despite the fact that it is level 1, the Regigigas still has a very low catch rate. This means you'll need to lower its health and give it a status effect before trying to catch it with anything other than a Master Ball. Once you've lowered Regigigas' health, you can use a status effect to help capture it. These Poke Balls will give you the best chance to catch the Regigigas. If you don't have either of these, use a Nest Ball or Ultra Ball.