Concept

Pentagram

A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle around the five points creates a similar symbol referred to as the pentacle, which is used widely by Wiccans and in paganism, or as a sign of life and connections. The word "pentagram" refers only to the five-pointed star, not the surrounding circle of a pentacle. Pentagrams were used symbolically in ancient Greece and Babylonia. Christians once commonly used the pentagram to represent the five wounds of Jesus. The word pentagram comes from the Greek word πεντάγραμμον (pentagrammon), from πέντε (pente), "five" + γραμμή (grammē), "line". Pentagram refers to just the star and pentacle refers to the star within the circle specifically although there is some overlap in usage. The word pentalpha is a 17th-century revival of a post-classical Greek name of the shape. Early pentagrams have been found on Sumerian pottery from Ur circa 3500 BCE, and the five-pointed star was at various times the symbol of Ishtar or Marduk. Pentagram symbols from about 5,000 years ago were found in the Liangzhu culture of China. The pentagram was known to the ancient Greeks, with a depiction on a vase possibly dating back to the 7th century BCE. Pythagoreanism originated in the 6th century BCE and used the pentagram as a symbol of mutual recognition, of wellbeing, and to recognize good deeds and charity. From around 300-150 BCE the pentagram stood as the symbol of Jerusalem, marked by the 5 Hebrew letters ירשלם spelling its name. The word Pentemychos (πεντέμυχος lit. "five corners" or "five recesses") was the title of the cosmogony of Pherecydes of Syros. Here, the "five corners" are where the seeds of Chronos are placed within the Earth in order for the cosmos to appear.

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Related concepts (22)
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean geometry to more than three dimensions and discovered all their convex regular polytopes, including the six that occur in four dimensions. The Schläfli symbol is a recursive description, starting with {p} for a p-sided regular polygon that is convex.
Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off. Take some corner or vertex of a polyhedron. Mark a point somewhere along each connected edge. Draw lines across the connected faces, joining adjacent points around the face. When done, these lines form a complete circuit, i.e. a polygon, around the vertex. This polygon is the vertex figure. More precise formal definitions can vary quite widely, according to circumstance.
Pentagon
In geometry, a pentagon (from the Greek πέντε pente meaning five and γωνία gonia meaning angle) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram. A regular pentagon has Schläfli symbol {5} and interior angles of 108°. A regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°).
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