Meaning of 嵌 in Japanese

あてはまる(atehamaru) 【当てはまる ·当て嵌まる】

(v5r) to apply (a rule); to be applicable; to come under (a category); to fulfill

はめる(hameru) 【嵌める ·填める ·篏める】

(v1, vt) to insert; to put in (such that there is a snug fit); to button; to put on (something that envelopes, e.g. gloves, ring)
to have sex; to fuck
一発で命中しなくたって、妊娠するまでハメ続ければいいだけだし。
Even if we don't get lucky on the first try we can just keep fucking till I get pregnant.
to pigeonhole (into a particular category)
to place a ring-shaped object around something (esp. one that restricts freedom, such as handcuffs)
to entrap; to set someone up (i.e. frame them for a crime, etc.)
おれ、うまくハメられた。
I was nicely framed.

はめこむ(hamekomu) 【はめ込む ·嵌め込む ·填め込む】

(v5m, vt) to inlay; to insert; to set
ダイアモンドは金の指輪にはめ込まれていた。
The diamond was set in a gold ring.
(math) to plug in (to a formula); to immerse
to trick; to deceive

あてはめる(atehameru) 【当てはめる ·当て嵌める】

(v1, vt) to apply; to adapt
この規則は貴方には当てはめることはできない。
This rule cannot be applied to you.

はまる(hamaru) · ハマる(hamaru) 【嵌まる ·填まる ·嵌る ·填る】

(v5r, vi) to fit; to get into; to go into
彼女は今度は自分が罠にはまった。
She fell into a trap in her turn.
to be fit for (a job, etc.); to be suited for; to satisfy (conditions)
to fall into; to plunge into; to get stuck; to get caught
to be deceived; to be taken in; to fall into a trap
to be addicted to; to be deep into; to be crazy about; to be stuck on