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In geometry, a generalized polygon can be called a **polygram**, and named specifically by its number of sides, so a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3} has 6 sides divided into two triangles.

A **regular polygram** {p/q} can either be in a set of **regular polygons** (for gcd(p,q)=1, q>1) or in a set of **regular polygon compounds** (if gcd(p,q)>1).^{[1]}

The polygram names combine a numeral prefix, such as *penta-*, with the Greek suffix *-gram* (in this case generating the word *pentagram*). The prefix is normally a Greek cardinal, but synonyms using other prefixes exist. The *-gram* suffix derives from *γραμμῆς* (*grammos*) meaning a line.^{[2]}

A regular polygram, as a general regular polygon, is denoted by its Schläfli symbol {*p*/*q*}, where *p* and *q* are relatively prime (they share no factors) and *q* ≥ 2. For integers *p* and *q*, it can be considered as being constructed by connecting every *q*th point out of *p* points regularly spaced in a circular placement.^{[3]}^{[4]}

{5/2} |
{7/2} |
{7/3} |
{8/3} |
{9/2} |
{9/4} |
{10/3}... |

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

Triangles... | Squares... | Pentagons... | Pentagrams... | ||||
---|---|---|---|---|---|---|---|

{6/2}=2{3} |
{9/3}=3{3} |
{12/4}=4{3} |
{8/2}=2{4} |
{12/3}=3{4} |
{10/2}=2{5} |
{10/4}=2{5/2} |
{15/6}=3{5/2} |

**^**Weisstein, Eric W. "Polygram".*MathWorld*.**^**γραμμή, Henry George Liddell, Robert Scott,*A Greek-English Lexicon*, on Perseus**^**Coxeter, Harold Scott Macdonald (1973).*Regular polytopes*. Courier Dover Publications. p. 93. ISBN 978-0-486-61480-9.**^**Weisstein, Eric W. "Polygram".*MathWorld*.

- Cromwell, P.;
*Polyhedra*, CUP, Hbk. 1997, ISBN 0-521-66432-2. Pbk. (1999), ISBN 0-521-66405-5. p. 175 - Grünbaum, B. and G.C. Shephard;
*Tilings and Patterns*, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1. - Grünbaum, B.; Polyhedra with Hollow Faces,
*Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993)*, ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70. - John H. Conway, Heidi Burgiel, Chaim Goodman-Strass,
*The Symmetries of Things*2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 404: Regular star-polytopes Dimension 2) - Robert Lachlan,
*An Elementary Treatise on Modern Pure Geometry*. London: Macmillan, 1893, p. 83 polygrams. - Branko Grünbaum,
*Metamorphoses of polygons*, published in*The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History*, (1994)