French term croix gamméea cross with arms shaped like the Greek letter gamma (Γ). Shortly thereafter, British antiquarians Edward Thomas and Robert Sewell separately published their studies about the symbol, using swastika as the common English term. The concept of a "reversed" swastika was probably first made among European scholars by Eugène Burnouf in 1852, and taken up by Schliemann in Ilios (1880), based on a letter from Max Müller that quotes Burnouf. The term sauwastika is used in the sense of "backwards swastika" by Eugène Goblet d'Alviella (1894): "In India it [the gammadion] bears the name of swastika, when its arms are bent towards the right, and sauwastika when they are turned in the other direction." Other names for the symbol include: tetragammadion (Greek: ) or cross gammadion (; French: ), as each arm resembles the Greek letter Γ () hooked cross (German: ), angled cross (), or crooked cross () cross cramponned, cramponnée, or cramponny in heraldry, as each arm resembles a crampon or angle-iron () fylfot, chiefly in heraldry and architecture tetraskelion (Greek: ), literally meaning 'four-legged', especially when composed of four conjoined legs (compare triskelion/triskele [Greek: ]) ugunskrusts (Latvian for "Fire Cross"; other namesCross of Fire, Pērkonkrusts (Cross of Thunder (Thunder Cross)), Cross of Perun (Cross of Perkūnas), Cross of Branches, Cross of Laima) whirling logs (Navajo): can denote abundance, prosperity, healing, and luck Appearance All swastikas are bent crosses based on a chiral symmetry, but they appear with different geometric details: as compact crosses with short legs, as crosses with large arms and as motifs in a pattern of unbroken lines. Chirality describes an absence of reflective symmetry, with the existence of two versions that are mirror images of each other. The mirror-image forms are typically described as left-facing or left-hand (卍) and right-facing or right-hand (卐). The compact swastika can be seen as a chiral irregular icosagon (20-sided polygon) with fourfold (90°) rotational symmetry. Such a swastika proportioned on a 5×5 square grid and with the broken portions of its legs shortened by one unit can tile the plane by translation alone. The Nazi swastika used a 5×5 diagonal grid, but with the legs unshortened. Written characters The swastika was adopted as a standard character in Chinese, "" () and as such entered various other East Asian languages, including Chinese script. In Japanese the symbol is called or . The swastika is included in