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,
Hexagon or circumradius, "R", which equals the side length, "t". The minimal diameter or the diameter of the inscribed circle (separation of parallel sides, flat-to-flat distance, short diagonal or height when resting on a flat base), "d", is twice the minimal radius or inradius, "r". The maxima and minima are related by the same factor: The area of a regular hexagon For any regular polygon, the area can also be expressed in terms of the apothem "a" and the perimeter "p". For the regular hexagon these are given by "a" = "r", and "p"formula_5, so The regular hexagon fills the fraction