Your description—spade-shaped leaves, light green with darker edges, vining habit, and pieces that regenerate when stuck in soil—points strongly to Oxalis, commonly called shamrock or wood sorrel. With many varieties (green, purple, variegated), a quick image search for "Oxalis houseplant" should confirm the ID.
Note how your plant differs (leaf shape, color pattern, flower description) or email a clear photo to a plant expert for precise ID and tailored care.
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