The first frieze group, F1, contains only translation symmetries. Mathematician John Conway created names that relate to footsteps for each of the frieze groups. According to Conway, F1 is also called a HOP.


Mosaic Border
Alcazar de los Reyes Cristianos
Cordoba, Spain

The second frieze group, F2, contains translation and glide reflection symmetries. According to Conway, F2 is called a STEP.


The third frieze group, F3, contains translation and vertical reflection symmetries. Conway named F3 a SIDLE.



Tile Frieze
Palacio de Velazquez
Parque de Retiro
Madrid, Spain

The fourth frieze group, F4, contains translation and rotation (by a half-turn) symmetries. According to Conway, F4 is called a SPINNING HOP.



Meander Frieze
San Giorgio Maggiore
Venice, Italy

The fifth frieze group, F5, contains translation, glide reflection and rotation (by a half-turn) symmetries. Conway calls F5 a SPINNING SIDLE.



Mosaic
Nuestra Senora de la Almundena
Madrid, Spain

The sixth frieze group, F6, contains translation and horizontal reflection symmetries. Conway named F6 a JUMP.



Ceiling
Mezquita
Cordoba, Spain

Finally, the seventh frieze group, F7, contains all symmetries (translation, horizontal & vertical reflection, and rotation). According to Conway, F7 is named a SPINNING JUMP.



Back of a Bench
Banos de la Maria de Padilla
Reales Alcazares
Seville, Spain
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