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Related to lattice space: Bravais lattice
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The space with repetitive units (of alternative attachment space and detachment space) is binary lattice space.
The combination of attachment space (1) and detachment space (0) results in three quantum space phases: miscible space, binary partition space, or binary lattice space for four-dimensional space-time.
Partch's 11-limit system exists in a four-dimensional lattice space, for example.