11. Similarly, has anyone proven that it's impossible to fit a regular pentagon inside a regular hexagon ? 12. A regular hexagon is defined as a hexagon that is both tangential ( has an inscribed circle ). 13. For instance, for " n " = 3, the permutohedron on three elements is just a regular hexagon . 14. A squares, or regular hexagons . 15. A regular hexagon can be extended into a regular dodecagon by adding alternating squares and equilateral triangles around it. 16. A regular hexagon can also be created as a truncated equilateral triangle, with Schl�fli symbol t { 3 }. 17. He found the closed form for side length of smallest regular hexagon that contains 4 circles of radius 1. 18. For example, the regular hexagon divides into 6 equilateral triangles and is the vertex figure for the regular triangular tiling. 19. The board is a regular hexagon with r = 6, which consists of 91 hexes; however, it is orientated horizontally. 20. It is a metal cap with a top shaped like an X rather than the regular hexagon of old caps.