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A hypercube is a graph whose nodes can be labeled by binary vectors such that the distance between the binary addresses in the graph is the Hamming distance. Due to the symmetry of the hypercube, one usually considers the graph embedded in the hypercube proportionally in distance, meaning that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>1</mn></msub></semantics></math></inline-formula>-graphs. In this paper, we determine the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>1</mn></msub></semantics></math></inline-formula>-embeddability of hypertrees and unicyclic hypergraphs.