What question did this study set out to answer?

To present space P3 as a new method for linearizing unit-cell parameters derived from axial lengths and interaxial angles.

February 22, 2026

P 3 , linearizing unit-cell parameters

Key Points

To present space P3 as a new method for linearizing unit-cell parameters derived from axial lengths and interaxial angles.
Introduced space P3 based on unit-cell axial lengths and interaxial angles.
Developed linearization techniques using three polar coordinate bases.
Compared P3 with more complex spaces like G6 and S6.
Successfully linearized unit-cell parameters using P3.
Demonstrated that P3 is more compact and interpretable than G6 and S6.

Abstract

The space P 3 is introduced, derived from unit-cell axial lengths and interaxial angles. P 3 enables linearization of unit-cell parameters using three polar coordinate bases. P 3 serves as a compact, interpretable alternative to more abstract spaces such as G 6 and S 6 .

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