p1m1 Frieze Pattern

Fourth frieze type; has horizontal mirror reflection symmetry parallel to translation axis but no rotation symmetry.

Neighborhood — ranked by edge-count

paper

framework

Seven Frieze Symmetry Groups
associated_with
Mathematical classification system for one-dimensional periodic patterns using group theory; core framework for the analysis.

concept

p111 Frieze Pattern
related_to
First of seven frieze types; has only translation symmetry, no rotations, reflections, or glide-reflections.
Frieze Patterns
related_to
The primary mathematical object of study; one-dimensional infinitely-repeating geometric patterns found in Islamic art.
p112 Frieze Pattern
related_to
Second frieze type; has two-fold rotational symmetry but no reflections or glide-reflections.
p1g1 Frieze Pattern
related_to
Seventh and rarest frieze type; has glide-reflection symmetry along translation axis but no rotation or reflection symmetry.
pm11 Frieze Pattern
related_to
Third frieze type; has vertical mirror reflection symmetry but no rotation symmetry.
pmm2 Frieze Pattern
related_to
Fifth frieze type; has reflection symmetry in two directions and two-fold rotational symmetry.
horizontal mirror
associated_with
Mirror line parallel to the translation axis (along the strip)

finding

Yeso border classified as p1m1 frieze pattern
associated_with
Plaster border with horizontal mirror on midline, no rotational symmetry, Figure 4

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

pmg2 Frieze Patternconcept0.846
Sixth frieze type; has two-fold rotational symmetry, vertical reflection symmetry, and glide-reflection symmetry.
No examples of p1g1 frieze pattern were found at the Real Alcázar in Sevillefinding0.806
Reported in Bodner's previous studies [4] and [5]
Seven frieze pattern groupsframework0.796
Classification of one-dimensional periodic patterns into 7 symmetry groups using international notation pxyz
Yeso wall panel classified as p1g1 frieze patternfinding0.755
Plaster wall panel with only glide-reflection symmetry, Figure 7
The p1g1 frieze class appears very rarely in Islamic mosaic tilings at the Alhambra and was entirely absent at Real Alcázar.finding0.744
Glazed tile border classified as pm11 frieze patternfinding0.740
Pattern with vertical mirrors at left and right edges of the primitive cell, Figure 3
Symmetries and frieze groups mathematically capture design pattern properties.claim0.726
Calligraphic inscription in Mexuar room classified as p111 frieze patternfinding0.724
Glazed tile inscription at summit of pillar, Figure 1; motto 'There is no victor but Allah'