Ancient Roman Sword of John the Revelator, surgical equipment to cut open a human corpse and sew it back up.
He kills depending on the Tableau (commonly stabbing).
Method of Disposal
The disposals were also dependent of the Tableau.
Since birth, Travis has had a psychological disorder that has made him extremely violent. He killed his parents at childhood then killed his Professor feeling that he was "invincible", then shut out the memory entirely. It is believed that he is using the Doomsday Killings simply in order to satisfy his need to kill, a "Justification" that he was searching for.
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The Doomsday Killer was the Main Antagonist of Season Six, whose kills are very decorative and religiously inspired. He sought to bring about the end of this world and the beginning of the new one by fulfilling specific Biblical Prophecies, which he believed would bring this into effect.