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Higher dimensions Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures: 4D 5D 4-simplex t0.svg The regular 5-cell (4-simplex) has five vertices and 10 edges. 4-simplex t1.svg The rectified 5-cell has 10 vertices and 30 edges. 5-simplex t1 A4.svg The rectified 5-simplex has 15 vertices, seen in this orthogonal projection as three nested pentagrams. 5-simplex t2 A4.svg The birectified 5-simplex has 20 vertices, seen in this orthogonal projection as four overlapping pentagrams. All ten 4-dimensional Schläfli–Hess 4-polytopes have either pentagrammic faces or vertex figure elements. Pentagram of Venus The pentagram of Venus The pentagram of Venus is the apparent path of the planet Venus as observed from Earth. Successive inferior conjunctions of Venus repeat with an orbital resonance of approximately 13:8—that is, Venus orbits the Sun approximately 13 times for every eight orbits of Earth—shifting 144° at each inferior conjunction.[34] The tips of the five loops at the center of the figure have the same geometric relationship to one another as the five vertices, or points, of a pentagram, and each group of five intersections equidistant from the figure's center have the same geometric relationship The Seal of Solomon (or Ring of Solomon; Arabic: ???? ??????? Khatam Sulayman) is the signet ring attributed to King Solomon in medieval Jewish tradition and in Islamic and Western occultism. It was often depicted in either a pentagram or hexagram shape; the latter also known as the Star of David in Jewish tradition. This ring variously gave Solomon the power to command demons, jinn (genies) and spirits, or to speak with animals. Due to the proverbial wisdom of Solomon, his signet ring, or its supposed design, it came to be seen as an amulet or talisman, or a symbol or character in medieval and Renaissance-era magic, occultism, and alchemy.
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