Talk:Equilateral pentagon

Some equilateral pentagons are being ignored

This page gives a pretty analysis of the possible shapes of equilateral pentagons in the plane. The graph in the "Two-dimensional mapping" section is particularly pretty. Unfortunately, at least one important class of equilateral pentagons -- those with precisely one pair of intersecting edges -- isn't covered by this analysis and isn't shown in the graph.

For an example of a shape that isn't covered, consider the point in the graph where α = 90 and β = 45. That point in the (α,β) plane is indicated by a dot a little way above the letter "C" in the label "Concave". Associated with that dot is a picture of a pentagon that has α = 90, β = 45, and δ = 23.9 degrees. The pentagon shown has edges that intersect only at their endpoints, the pentagon vertices. But there is another pentagon that also has α = 90, β = 45, and δ = 23.9. To construct that other pentagon, take the vertex at which the angle is δ and flip it over, from the upper left to the lower right, leaving all other vertices fixed. The result will be a pentagon with a single pair of edges that intersect -- a pentagon that is not shown anywhere in the graph.

LyleRamshaw (talk) 16:29, 27 August 2014 (UTC)