Isotoxal figure 2-dimensional tessellation constructed from regular polygons is isotoxal. For instance, the truncated icosahedron (the familiar soccerball) has two types of edges: hexagon-hexagon and hexagon-pentagon, and it is not possible for a symmetry of the solid to move a hexagon-hexagon edge onto a hexagon-pentagon edge. An isotoxal polyhedron has the same dihedral angle for all edges. There are nine convex isotoxal polyhedra formed from the Platonic solids, 8 formed by the Kepler–Poinsot polyhedra, and six more as quasiregular (3 | p q) star polyhedra and their duals. There are at least 5 polygonal tilings of the Euclidean plane that are isotoxal,
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"