Vertical
When a thread loiters on the horns of a coat rack, it's always vertical. By loitering I mean hanging around, and by horns I mean the little bits sticking off a coat rack that you hang your vertical threads on. Obviously.
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Whether or not a thread will hang vertical depends on how you 立てる (たて) your coat rack. If you 立てる the coat rack properly, the threads will hang off it in a perfectly vertical way. On the other hand, if you 立てる it carelessly, things might end up kind of kind of diagonal and weird.