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 hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation. In addition to the regular hexagon, which determines a unique tessellation of the plane, any irregular hexagon which satisfies the Conway criterion will tile the plane. Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the "Pascal line" of that configuration. The Lemoine hexagon is a cyclic hexagon (one inscribed in a