The Unfinished Vault (named Fake Vault 13 in-game) is a small cave with some construction signs for what was to be a Vault-Tec Industries Vault, but was not finished before the Great War. Its intended number is unknown, but may have been the first location of Vault 13 before its relocation. It must be noted that the cave for the fake Vault 13 looks exactly like the cave for the real Vault 13.
The directions to this place can be learned from the "Vault 13 Holodisk", which can be bought from Merk in the New California Republic (Shady Sands) for $1000.
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The Unfinished Vault appears only in Fallout 2.