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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.

Digonpolygon with 2 edges
Trianglepolygon with 3 edges
Squarepolygon with 4 edges
Pentagonpolygon with 5 edges
Hexagonpolygon with 6 edges
Heptagonpolygon with 7 edges
Octagonpolygon with 8 edges
Nonagonpolygon with 9 edges
Decagonpolygon with 10 edges
Undecagonpolygon with 11 edges
Dodecagonpolygon 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.
This loads the package.
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An octagon has 8 edges.
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This is the area of an octagon when the length of each edge is 1.
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These points represent the coordinates of the vertices of an octagon.
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Here is a plot of the vertices of an octagon.
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