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Gagarin's spacecraft was known as Vostok 3KA-2 (Vostok 1).
Yuri Gagarin was carried to space in the Vostok-1 spacecraft (a Vostok 3KA spacecraft), which was carried into space onboard a Vostok-K (more specifically a Vostok-8K72K) rocket.
Vostok I
Vostok I.
Vostok 3KA-2, also known as Vostok 1.