Researchers have introduced a novel geometric framework designed to enhance the visualization of multi-qubit pure quantum states, specifically focusing on two- and three-qubit systems. This approach addresses the long-standing challenge of intuitively representing complex quantum states beyond the single-qubit Bloch sphere, which inherently lacks the capacity for multi-qubit configurations. The proposed framework uniquely separates the local degrees of freedom from the entanglement degrees of freedom, providing a clearer understanding of how these distinct properties contribute to the overall state structure1. This explicit disentanglement of local properties from the non-local phenomenon of entanglement is crucial for dissecting the intricate nature of quantum information, making it more accessible for both advanced research and educational purposes. By offering a unified and more detailed visualization method, this work aims to deepen insights into quantum mechanics. This improved ability to model and understand complex quantum states is critical for advancing quantum computing, where the precise manipulation of entanglement holds the key to developing powerful new computational paradigms, fundamentally altering future cryptographic and computational landscapes.