concept
active
concept:p1g1-frieze-patternp1g1 Frieze Pattern
Seventh and rarest frieze type; has glide-reflection symmetry along translation axis but no rotation or reflection symmetry.
Neighborhood — ranked by edge-count
Papers (1)
paper
- Frieze Patterns of the Alhambramentions
Frameworks (1)
framework
- Seven Frieze Symmetry Groupsassociated_withMathematical classification system for one-dimensional periodic patterns using group theory; core framework for the analysis.
Concepts (5)
concept
- p111 Frieze Patternrelated_toFirst of seven frieze types; has only translation symmetry, no rotations, reflections, or glide-reflections.
- p1m1 Frieze Patternrelated_toFourth frieze type; has horizontal mirror reflection symmetry parallel to translation axis but no rotation symmetry.
- p112 Frieze Patternrelated_toSecond frieze type; has two-fold rotational symmetry but no reflections or glide-reflections.
- pmg2 Frieze Patternrelated_toSixth frieze type; has two-fold rotational symmetry, vertical reflection symmetry, and glide-reflection symmetry.
- Glide-Reflection Symmetryassociated_withOne of four key isometries; combination of reflection and translation parallel to the mirror line.
Findings (3)
finding
- Reported in Bodner's previous studies [4] and [5]
- p1g1 class appears very rarely in planar mosaic tilingsassociated_withBased on statistical distribution chart in Abas & Salman; two of three rarest wallpaper groups involve glide-reflections (pg and pmg)
- Yeso wall panel classified as p1g1 frieze patternassociated_withPlaster wall panel with only glide-reflection symmetry, Figure 7
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.
- Third frieze type; has vertical mirror reflection symmetry but no rotation symmetry.
- Fifth frieze type; has reflection symmetry in two directions and two-fold rotational symmetry.
- Classification of one-dimensional periodic patterns into 7 symmetry groups using international notation pxyz
- Plaster border with horizontal mirror on midline, no rotational symmetry, Figure 4
- Pattern with vertical mirrors at left and right edges of the primitive cell, Figure 3