Polygram (geometry)


In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides, so a regular pentagram,, has 5 sides, and the regular hexagram, or 2 has 6 sides divided into two triangles.
A regular polygram can either be in a set of [|regular polygons] or in a set of regular polygon compounds.

Etymology

The polygram names combine a numeral prefix, such as ', with the Greek suffix '. The prefix is normally a Greek cardinal, but synonyms using other prefixes exist. The -gram suffix derives from γραμμῆς meaning a line.

Generalized regular polygons

A regular polygram, as a general regular polygon, is denoted by its Schläfli symbol, where p and q are relatively prime and q ≥ 2. For integers p and q, it can be considered as being constructed by connecting every qth point out of p points regularly spaced in a circular placement.

Pentagram|
Heptagram|
Heptagram|
Octagram|
Enneagram |
Enneagram |
Enneagram |...

Regular compound polygons

In other cases where n and m have a common factor, a polygram is interpreted as a lower polygon,, with k = gcd, and rotated copies are combined as a compound polygon. These figures are called regular compound polygons.