1.8617, where (golden ratio). The is obtained because each iteration has 6 pentagons that are scaled by . The boundary of a pentaflake is the Koch curve of 72 degrees. There is also a variation of the pentaflake that has no central pentagon. Its Hausdorff dimension equals ≈ 1.6723. This variation still contains infinitely many Koch curves, but they are somewhat more visible. Concentric patterns of pentaflake boundary shaped tiles can cover the plane, with the central point being covered by a third shape formed of segments of 72-degree Koch curve, also with 5-fold rotational and reflective symmetry. Hexaflake A hexaflake, is formed by successive flakes of seven regular hexagons. Each flake is formed by placing a scaled hexagon in each corner and one in the center. Each iteration has 7 hexagons that are scaled by 1/3. Therefore the hexaflake has 7n−1 hexagons in its nth iteration, and its Hausdorff dimension is equal to ≈ 1.7712. The boundary of a hexaflake is the standard Koch curve of 60 degrees and infinitely many Koch snowflakes are contained within. Also, the projection of the cantor cube onto the plane orthogonal to its main diagonal is a hexaflake. The hexaflake has been applied in the design of antennas and optical fibers. Like the pentaflake, there is also a variation of the hexaflake, called the Sierpinski hexagon, that has no central hexagon. Its Hausdorff dimension equals ≈ 1.6309. This variation still contains infinitely many Koch curves of 60 degrees. Polyflake n-flakes of higher polygons also exist, though they are less common and don't usually have a central polygon. Some examples are shown below; the 7-flake through 12-flake. While it may not be obvious, these higher polyflakes still contain infinitely many Koch curves, but the angle of the Koch curves decreases as n increases. Their Hausdorff dimensions are slightly more difficult to calculate than lower n-flakes because their scale factor is less obvious. However, the Hausdorff dimension is always less than two but no less than one. An interesting n-flake is the ∞-flake, because as the value of n increases, an n-flake's Hausdorff dimension approaches 1, In three dimensions n-flakes can generalized to higher dimensions, in particular to a topological dimension of three. Instead of polygons, regular polyhedra are iteratively replaced. However, while there are an infinite number of regular polygons, there are only five regular, convex polyhedra. Because of this, three-dimensional n-flakes are also