Polytopes Package
Polytopes Package
As of Version 12.0, all the functionality of the Polytopes package is built into the Wolfram System. »
This package contains functions that give geometrical characteristics of regular polygons. Polygons are identified by name (Digon, Decagon, etc.) in function arguments and in results.
| NumberOfVertices[p] | number of vertices in polygon  |
| NumberOfEdges[p] | number of edges in polygon  |
| NumberOfFaces[p] | number of faces in polygon  |
| Vertices[p] | list of vertex coordinates for polygon  |
| Area[p] | area of polygon  when edges have unit length |
| InscribedRadius[p] | radius of the inscribed circle of polygon  when edges have unit length |
| CircumscribedRadius[p] | radius of the circumscribed circle of polygon  when edges have unit length |
| Faces[p] | list of faces from vertex numbers for polygon  |
Geometrical characteristics of polygons.
| Digon | polygon with 2 edges |
| Triangle | polygon with 3 edges |
| Square | polygon with 4 edges |
| Pentagon | polygon with 5 edges |
| Hexagon | polygon with 6 edges |
| Heptagon | polygon with 7 edges |
| Octagon | polygon with 8 edges |
| Nonagon | polygon with 9 edges |
| Decagon | polygon with 10 edges |
| Undecagon | polygon with 11 edges |
| Dodecagon | polygon with 12 edges |
The functions Area, InscribedRadius, and CircumscribedRadius give information for a polygon with edges of length 1. The list of coordinates returned by Vertices is conventional for the specified polygon and does not necessarily correspond to a polygon with unit edge length.