This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 POLYTOPES PACKAGE TUTORIAL | Functions »

# Polytopes Package

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 p NumberOfEdges[p] number of edges in polygon p NumberOfFaces[p] number of faces in polygon p Vertices[p] list of vertex coordinates for polygon p Area[p] area of polygon p when edges have unit length InscribedRadius[p] radius of the inscribed circle of polygon p when edges have unit length CircumscribedRadius[p] radius of the circumscribed circle of polygon p when edges have unit length Faces[p] list of faces from vertex numbers for polygon p

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

Names of polygons.

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.
An octagon has 8 edges.
 Out[2]=
This is the area of an octagon when the length of each edge is 1.
 Out[3]=
These points represent the coordinates of the vertices of an octagon.
 Out[4]=
Here is a plot of the vertices of an octagon.
 Out[5]=