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Also, the ratio of the length of the shorter segment to the segment bounded by the two intersecting edges (a side of the pentagon in the pentagram's center) is φ.As the four-color illustration shows: The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles.Aleister Crowley made use of the pentagram in his Thelemic system of magick: an adverse or inverted pentagram represents the descent of spirit into matter, according to the interpretation of Lon Milo Du Quette.Crowley contradicted his old comrades in the Hermetic Order of the Golden Dawn, who, following Levi, considered this orientation of the symbol evil and associated it with the triumph of matter over spirit.The decision was made following ten applications from families of fallen soldiers who practiced Wicca.The government paid the families The five pointed star is a symbol of the Serer religion and the Serer people of West Africa.

Groups of five intersections of curves, equidistant from the figure's center, have the same geometric relationship.Based on Renaissance-era occultism, the pentagram found its way into the symbolism of modern occultists.Following Anton La Vey, and ultimately based on a drawing by French nobleman and occultist Stanislas de Guaita (La Clef de la Magie Noire, 1897), the Sigil of Baphomet, a pentagram with two points up inscribed in a double circle with the head of a goat inside the pentagram is the copyrighted logo of the Church of Satan.Other temples decorated with five-pointed stars in both orientations include the Salt Lake Temple and the Logan Utah Temple.These usages come from the symbolism found in Revelation chapter 12: "And there appeared a great wonder in heaven; a woman clothed with the sun, and the moon under her feet, and upon her head a crown of twelve stars." The encircled pentagram (referred to as a pentacle by the plaintiffs) was added to the list of 38 approved religious symbols to be placed on the tombstones of fallen service members at Arlington National Cemetery on 24 April 2007.

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The golden ratio, φ = (1 √5) / 2 ≈ 1.618, satisfying plays an important role in regular pentagons and pentagrams.