In terrestrial and Martian periglacial environments, networks of more or less regular polygonally shaped fracture patterns characterise the wide areas of the ground. Figure 1 and 2 show the remarkable resemblance of these polygonal patterns on Earth and on Mars.

In terrestrial permafrost regions, polygonal crack patterns develop generally due to the contraction of permafrost material caused by a rapid temperature drop and leading to fissures and cracks that are subsequently filled with ice. [van Gasselt, 2007; Lachenbruch, 1962; French, 1996]. The building of ice-filled fissures generally takes several years. Initial fissures might close during spring season. However, these fissures are weak zones supporting their re-opening during the next freezing period. Within these fissures, penetrating melt water is freezing and produces a vertical ice vein [van Gasselt, 2007]. The resulting ice-wedges grow during several freeze-thaw cycles (Fig. 3) and might reach widths of up to four meters and depths of several tens of meters [French, 1996].

Sand or soil wedges can develop if moisture supply or temperature conditions are not adequate for the development of ice wedges. In these cases, windblown sediments (sand, soil) are the infilling mediums [French, 1996].
Polygonal patterns form though the lateral propagation and interconnection of the ice-filled fractures, intersecting at characteristic angels. Depending on the angle of intersection, orthogonal, hexagonal or tetragonal patterns can develop [Lachenbruch, 1962, 1966].
Terrestrial polygonal cells vary in diameter from a few decimetres up to a few metres and more, whereas the fractures can reach depths of several decimetres up to 10m, depending besides other factors on the climatic regime and water or ice input. [van Gasselt, 2007; French, 1996].

Although the formation requires seasonally liquid water, the Martian polygonal features are interpreted as thermal contraction polygons or ice-wedge polygons, as well, owing to their remarkable resemblance to the terrestrial counterparts [e.g. Lucchitta, 1981].The diameters of the Martian polygonal features range from a few metres to several hundred metres. According to the distribution of periglacial permafrost environments, polygonal patterns on Mars can be observed in the mid-latitudes between 38° and 70° north and south, and in the south polar region [van Gasselt, 2007].

The latest images of polygonal patterns on Mars were taken by NASA's Phoenix Mars Lander located in the vast plains of Vastitas Borealis in the northern lowlands. Figure 5 shows a flat landscape strewed with tiny pebbles and polygonal cracking [www3]. The closer look (Fig. 6) confirms the polygonal pattern on the ground, which looks similar to the icy ground of the terrestrial arctic regions [www4].