Hexagon allowing the result to "fold up". The Archimedean solids with some hexagonal faces are the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron. These hexagons can be considered truncated triangles, with Coxeter diagrams of the form and . There are other symmetry polyhedra with stretched or flattened hexagons, like these Goldberg polyhedron G(2,0): There are also 9 Johnson solids with regular hexagons: Hexagon In geometry, a hexagon (from Greek ἕξ "hex", "six" and γωνία, "gonía", "corner, angle") is a six-sided polygon or 6-gon. The total of the internal angles of
Pappus's hexagon theorem Pappus's hexagon theorem In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points "A", "B", "C", and another set of collinear points "a", "b", "c", then the intersection points "X", "Y", "Z" of line pairs "Ab" and "aB", "Ac" and "aC", "Bc" and "bC" are collinear, lying on the "Pappus line". These three points are the points of intersection of the "opposite" sides of the hexagon "AbCaBc". It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring. Projective planes in which the "theorem"