page_title: Rhombille tiling
section_title: Artistic and decorative applications
hierarchical_section_title: Rhombille tiling / Artistic and decorative applications
caption_attribution_description: AWIB-ISAW: Houses on Delos (XLII) A cubic floor mosaic in a house on the Greek island of Delos. by Irene Soto (2010) copyright: 2010 Irene Soto (used with permission) photographed place: Delos (Delos) [1] Published by the Institute for the Study of the Ancient World as part of the Ancient World Image Bank (AWIB). Further information: [2].
context_page_description: In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets of six rhombi meet at their 60° angles.
context_section_description: The rhombille tiling can be interpreted as an isometric projection view of a set of cubes in two different ways, forming a reversible figure related to the Necker Cube. In this context it is known as the "reversible cubes" illusion.
  In the M. C. Escher artworks Metamorphosis I, Metamorphosis II, and Metamorphosis III Escher uses this interpretation of the tiling as a way of morphing between two- and three-dimensional forms. In another of his works, Cycle (1938), Escher played with the tension between the two-dimensionality and three-dimensionality of this tiling: in it he draws a building that has both large cubical blocks as architectural elements (drawn isometrically) and an upstairs patio tiled with the rhombille tiling. A human figure descends from the patio past the cubes, becoming more stylized and two-dimensional as he does so. These works involve only a single three-dimensional interpretation of the tiling, but in Convex and Concave Escher experiments with reversible figures more generally, and includes a depiction of the reversible cubes illusion on a flag within the scene.
  The rhombille tiling is also used as a design for parquetry and for floor or wall tiling, sometimes with variations in the shapes of its rhombi. It appears in ancient Greek floor mosaics from Delos and from Italian floor tilings from the 11th century, although the tiles with this pattern in Siena Cathedral are of a more recent vintage. In quilting, it has been known since the 1850s as the "tumbling blocks" pattern, referring to the visual dissonance caused by its doubled three-dimensional interpretation. As a quilting pattern it also has many other names including cubework, heavenly stairs, and Pandora's box. It has been suggested that the tumbling blocks quilt pattern was used as a signal in the Underground Railroad: when slaves saw it hung on a fence, they were to box up their belongings and escape. See Quilts of the Underground Railroad. In these decorative applications, the rhombi may appear in multiple colors, but are typically given three levels of shading, brightest for the rhombs with horizontal long diagonals and darker for the rhombs with the other two orientations, to enhance their appearance of three-dimensionality.
  There is a single known instance of implicit rhombille and trihexagonal tiling in English heraldry – in the Geal/e arms.
caption: Rhombille tiling floor mosaic in Delos
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