gate
闥 centers on a gate or doorway, specifically a small gate or side door within a larger gate complex.
闥 combines 門 (gate) with 達, which likely contributes the sound and may suggest reaching or passing through, fitting a small gate that allows passage.
The outer 門 is a large gate, and inside is 達 (reach, arrive). Picture a small side gate within the big gate that you reach to pass through quickly.
For タツ, imagine a small gate that a cat uses: cat -> タツ, and the cat slips through the side door.
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