Many Segovian facades have been decorated with sgraffiti long since, characterizing her own aesthetic and popular architecture. Most of these sgraffiti are repetition patterns -periodic mosaics and friezes- that can be studied from the point of view of symmetry.

The mathematical theory of symmetry, developed at the beginning of the 20th century, classifies the friezes of the plane in 17 algebraic groups, named friezes groups, and the periodic mosaics in 17 algebraic groups: the wallpaper symmetry groups. Given a frieze or mosaic model, the symmetries -translations, reflections, rotations, glides- that leave the model unchanged, are used to identitfy its symmetry group.

The Real Street go from Mayor Place (near the Cathedral) until Azoguejo Place (near the Roman Aqueduct). It is composed by different stretchs: Isabel La Católica Street, Corpus Christi Place, Juan Bravo Street and Cervantes Street.

Walking on this route you can see many different sgraffiti models and enjoy identifying their symmetry group.

Do you want to find in Segovia's Real Street the models below?

Some friezes

You can see below: horizontal translations, 2-rotation centers (180º), the central reflection axis, many vertical reflection axes through 2-centers.

You can see below: horizontal translations, 2-rotation centers (180º), the central glide axis and many vertical reflection axes.

You can see below: horizontal translations, many vertical reflection axes. Nor rotations nor glides.

You can see below: horizontal translations and 2-rotation centers (180º). Nor reflections nor glides.

You can see below: horizontal translations. Nor rotations nor reflections nor glides.

Some mosaics

The next is a mosaic whose symmetry group is named p6m.

You can see in it: translations, 6-rotation centers (60º), 3-rotation centers (120º), 2-rotation centers (180º), reflection axes through each center, and (difficulty) many glide axes.

Next: Some mosaics whose symmetry group is named p4m.

You can see in them: translations, 4-rotation centers (90º), 2-rotation centers (180º), reflection axes through each center and (difficulty) some glide axes trhough 2-centers.

The next: A mosaic whose symmetry group is named p4g.

You can see in it: translations, 4-rotation centers (90º), 2-rotation centers (180º), reflection axes through each 2-center and (difficulty) glide axes nor through rotation centers.

The next: A mosaic whose symmetry group is named p4.

You can see in it: translations, 4-rotation centers (90º) and 2-rotation centers. They aren´t reflections nor glides.

The next: Two mosaics wshose symmetry group is named pmm.

You can see in them: translations, 2-rotation centers (180º), vertical reflection axes and horizontal reflections axes through rotation centers.They aren´t glides.

The next: A mosaic whose symmetry group is pmg.

You can see in it: translations, 2-rotation centers (180º), horizontal glide axes through rotation centers and vertical reflection axes nor through them.

The next: A mosaic whose symmetry group is named p2.

You can see in it: translations and 2-rotation centers (180º). They aren´t reflections nor glides.

The next: Mosaics whose symmetry group is named cm.

You can see in them: translations, vertical reflection axes, and (difficulty) vertical glide axes. They aren´t rotations.

The next is the unique mosaic model in this town whose symmetry group is pm.

You can see in it: translations and vertical reflection axes.They aren´t rotations nor glides.

The next: Two mosaics whose symmetry group is p1.

They are only translations. They aren´t rotations, nor reflections nor glides.

Additional lectures on symmetry groups , or sgraffiti  technique, or Segovia .