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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.
To Jews and the enemies of Nazi Germany, it became a symbol of antisemitism and terror. The earliest known textual use of the word swastika is in Panini's Ashtadhyayi, where it is used to explain one of the Sanskrit grammar rules, in the context of a type of identifying mark on cow's ear.Textile number T.231-1923 held at the V&A Museum in London includes small swastikas in its design.This piece was found at Qau-el-Kebir, near Asyut, and is dated between AD 300 and 600.Indo-Iranians, Celts, Greeks, Germanic peoples and Slavs.In Sintashta culture's "Country of Towns", ancient Indo-European settlements in southern Russia, it has been found a great concentration of some of the oldest swastika patterns.According to Reza Assasi, the swastika is a geometric pattern in the sky representing the north ecliptic pole centred to Zeta Draconis.
He argues that this primitive astrological symbol was later called the four-horse chariot of Mithra in ancient Iran and represented the centre of Ecliptic in the star map and also demonstrates that in Iranian mythology, the cosmos was believed to be pulled by four heavenly horses revolving around a fixed centre on clockwise direction possibly because of a geocentric understanding of an astronomical phenomenon called axial precession.
He suggests that this notion was transmitted to the west and flourished in Roman mithraism in which this symbol appears in Mithraic iconography and astrological representations.
Carl Sagan in his book Comet (1985) reproduces Han period Chinese manuscript (the Book of Silk, 2nd century BC) that shows comet tail varieties: most are variations on simple comet tails, but the last shows the comet nucleus with four bent arms extending from it, recalling a swastika.
Another hypothesis is that the four arms of the cross represent four aspects of nature - the sun, wind, water, soil.
Some have said the four arms of cross are four seasons, where the division for 90-degree sections correspond to the solstices and equinoxes.
under the commonly used IAST transliteration system, but is pronounced closer to "swastika" when letters are used with their English values. Left: a left facing swastika, also called counterclockwise, appears in the Bon tradition; Right: a right facing swastika, typically called clockwise, appears commonly in Hinduism, Buddhism and Jainism.