| 词条 | Polygram (geometry) | |||||||||||||||||||||||
| 释义 |
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] EtymologyThe 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] Generalized regular polygons{{Further information|Regular_polygon#Regular_star_polygons}}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 qth point out of p points regularly spaced in a circular placement.[3][4]
Regular compound polygons{{Further information|List_of_regular_polytopes_and_compounds#Two_dimensions}}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.
See also
References1. ^{{Mathworld |urlname=Polygram |title=Polygram}} 2. ^γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus 3. ^{{cite book |last=Coxeter |first=Harold Scott Macdonald |title=Regular polytopes |publisher=Courier Dover Publications|page=93 |year=1973 |isbn=978-0-486-61480-9}} 4. ^{{MathWorld |urlname=polygram |title=Polygram}}
2 : Polygons|Star symbols |
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