I tried to be thorough.
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The Excruciatingly Complete Quadrilateral Classification Flowchart
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This entry was posted in Mathematics and tagged chart, flowchart, geometry, Mathematics, quadrilateral, rectangle, rhombus, square, trapezoid. Bookmark the permalink.
My husband, the rocket scientist, was really impressed by the hard work that went into this flow chart. He is not a blogger but we are both impressed. As an artist and writer, I am both fascinated and awed by your blog. I am trying hard to get my right brain to appreciate and work in common with my left brain more.
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Nice flow chart, but it it is incomplete, doesn’t include self-intersecting cases.
Many exist as vertex figures of the uniform star polyhedra, and dual uniform star faces.
http://gratrix.net/polyhedra/uniform/summary/
Also one example here:
http://en.wikipedia.org/wiki/Antiparallelogram
For the missing intersecting cases, I like “crossed” prefixed names, modifed from their convex names, which could have many possible forms, although you could also qualify which set of edges are retained in some cases.
crossed-square, crossed-rectangle
crossed-isosceles trapezoid, crossed-trapezoid
crossed-kite, crossed-dart
crossed-parallelogram
crossed-rhombus
crossed-quadrilateral
I couldn’t guess how to fit them all into your chart, although you could simply start with asking if it was self-intersecting, and do a fully parallel flow chart for such cases!
p.s. I also like this visual chart for convex cases based on symmetry, comes from John Conway’s book the Symmetries of Things.
http://commons.wikimedia.org/wiki/File:Symmetries_of_square.svg
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