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
Dehn plane is π. This is Dehn's semi-Euclidean geometry. It is discussed in . In the same paper, Dehn also constructed an example of a non-Legendrian geometry where there are infinitely many lines through a point not meeting another line, but the sum of the angles in a triangle exceeds π. Riemann's elliptic geometry over Ω("t") consists of the projective plane over Ω("t"), which can be identified with the affine plane of points ("x":"y":1) together with the "line at infinity", and has the property that the sum of the angles of any triangle is greater than π The non-Legendrian geometry consists of