octagrams

An octagram is an eight-pointed star polygon. It can be represented by connecting vertices of a regular octagon. There are two regular octagrams. The first, denoted as {8/3}, is formed by connecting every third vertex of a regular octagon. The second, {8/4}, is degenerate as it consists of two separate squares. Other less common octagrams can be formed by connecting vertices of a non-regular octagon or by using different connection patterns.

Octagrams appear in various contexts. In religious symbolism, the octagram can represent concepts such as regeneration, Christ, or the eight beatitudes in Christianity, and the eightfold path in Buddhism. In heraldry, the octagram is sometimes referred to as a star or starburst. It can also be found in art and design, often used for its aesthetic appeal.

Mathematically, octagrams are a type of star polygon. The notation {n/m} is used to describe a star polygon, where n is the number of vertices of the regular polygon and m is the step size used to connect the vertices. For an octagram, n=8. Thus, {8/3} represents the regular octagram formed by connecting every third vertex. The degenerate octagram {8/4} is formed by connecting every fourth vertex, which results in two superimposed squares. Higher values of m for n=8 would repeat these patterns.

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