A main feature of Islamic art is the use of infinitely-repeating geometric figures to cover planar surfaces. Some form two-dimensional “wallpaper” patterns and others appear in one-dimensional frieze patterns. The walls and ceilings of the palaces of the Alhambra contain an abundance of original and restored examples of both types of geometric ornament that are recognizably Islamic in character. This paper will consider only frieze patterns, presenting and analyzing a few beautiful examples from the Alhambra.