2 thoughts on “The Excruciatingly Complete Quadrilateral Classification Flowchart”

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.

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!

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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