framework
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framework:seven-frieze-pattern-groupsSeven frieze pattern groups
Classification of one-dimensional periodic patterns into 7 symmetry groups using international notation pxyz
Neighborhood — ranked by edge-count
Papers (1)
paper
- Frieze Patterns of the Alhambramentions
Methods (1)
method
- International Symbol Notation (pxyz)implementsStandardized notation system for describing and classifying the seven frieze pattern groups using letters and numbers.
Frameworks (1)
framework
- Seven Frieze Symmetry Groupsrelated_tosame_asMathematical classification system for one-dimensional periodic patterns using group theory; core framework for the analysis.
Findings (1)
finding
- Author's survey of Alhambra ornamentation yielded all seven types
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- The primary mathematical object of study; one-dimensional infinitely-repeating geometric patterns found in Islamic art.
- Seventh and rarest frieze type; has glide-reflection symmetry along translation axis but no rotation or reflection symmetry.
- Fourth frieze type; has horizontal mirror reflection symmetry parallel to translation axis but no rotation symmetry.
- First of seven frieze types; has only translation symmetry, no rotations, reflections, or glide-reflections.
- Second frieze type; has two-fold rotational symmetry but no reflections or glide-reflections.
- Sixth frieze type; has two-fold rotational symmetry, vertical reflection symmetry, and glide-reflection symmetry.
- Third frieze type; has vertical mirror reflection symmetry but no rotation symmetry.