Frieze groups

The frieze groups are used to classify patterns which are repetitive in one direction, according to their symmetries. Of course, such designs occur frequently in architecture and decorative art. Mathematical study of such patterns reveals that essentially, only seven types of symmetry can occur.

The first frieze group, coined HOP by John Conway, is generated by a single translation and therefore contains only translational symmetries:

The second group, STEP, contains translation and glide reflection symmetries. This group is singly generated as well, by a glide reflection (as a translation can be simulated by two glide reflections).

SIDLE contains translation and vertical reflection symmetries.

Next, a SPINNING HOP is generated by a translation and a 180° rotation.

SPINNING SIDLE contains translation, glide reflection and rotation (by a half-turn) symmetries.

JUMP contains translation and horizontal reflection symmetries.

Finally, SPINNING JUMP contains all symmetries (translation, horizontal & vertical reflection, and rotation). This group requires three generators, for instance a translation, the reflection in the horizontal axis and a reflection across a vertical axis.

1,500-year-old frieze with human figures found at Peru shrine

LIMA (AFP).- Archaeologists in Peru have unearthed a 1,500-year old frieze with human figures believed to be from the indigenous Moche culture, the latest find at a site famous for its pre-Incan treasures.

The discovery, in Peru’s northern La Libertad region, was made at the Huaca de la Luna, or Shrine of the Moon, the El Comercio newspaper reported on Sunday.

Ten sculpted human figures on the work measure 1.6 meters (roughly 5'3") tall, archaeologists working at the site told the paper.

The Huaca de La Luna sanctuary, which pre-dates the Spanish conquest, is located a few kilometers (miles) outside the current city of Trujillo and is a site rich in ancient archaeological treasures. Read more.

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