छिद्

छिदिँर् = छ इ द इ चंद्र बिंदी र
छि = (not walking, not repeating, not knotted, drill, moving at one place only; many+tiny) + below/objectified
दी = (roll/throw/give) + below
चंद्र बिंदी for ञ or ङ or म = surface/outside/inside
र = sharp
Hence
drill below roll/give below sharp = cut below, hew off, rend, split, pierce, separate

धातु अर्थ
at द्वैधीकरण = द्वैध making = द्व + ऐ as स्वर विभक्ति (षष्टि = contineuous connection) + ध =द्व स्य ध = carrying of द्व
It can mean carrying of two.
It can also mean carry of give wave like movcement.

रूढ अर्थ