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Geometry`Polytopes`

This package contains functions that give geometrical characteristics of regular polygons and regular polyhedra. Polygons and polyhedra are identified by name (Square, Tetrahedron, etc.) in function arguments and in results.

Geometrical characteristics of polygons.

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.

In[1]:= << Geometry`Polytopes`

An octagon has 8 edges.

In[2]:= NumberOfEdges[Octagon]

Out[2]=

This is the area of an octagon when the length of each edge is 1.

In[3]:= Area[Octagon]

Out[3]=

These points represent the coordinates of the vertices of an octagon.

In[4]:= Vertices[Octagon]

Out[4]=

Here is a plot of the vertices of an octagon.

In[5]:= Show[Graphics[{PointSize[.05], Point /@ %},
AspectRatio -> 1]]

Out[5]=

The polyhedra functions Volume, InscribedRadius, and CircumscribedRadius return information for a polyhedron with edges of length 1. The list of coordinates returned by Vertices is conventional for the specified polyhedron and does not necessarily correspond to a polyhedron with unit edge length.

Geometrical characteristics of polyhedra.

The five regular polyhedra.

This is the volume of a tetrahedron with edges of length 1.

In[6]:= Volume[Tetrahedron]

Out[6]=

These coordinates form the vertices of an octahedron.

In[7]:= Vertices[Octahedron]

Out[7]=