Hexnet Hexagonal Tag Feed: symmetry A feed of tagged nodes. https://hexnet.org/blog The permutohedron <p> We seem to have fallen a bit behind in terms of keeping this site updated with RELEVANT MATHEMATICAL INFORMATION about hexagons. This is a deficit we're looking to correct as soon as possible. First up, let us consider the permutohedra. We at HEXNET.ORG have been meaning to write something about permutohedra for a couple of years now, but have never really found a good opportunity to so. WE WILL NOT EXPEND GREAT EFFORT DOING SO NOW. It will suffice to merely describe the concept in conjunction with some helpful imagery, which will hopefully serve as a useful foundation for further geometrical observations and investigations in the near future. </p> Sun, 26 May 2013 18:10:58 +0000 https://hexnet.org/content/permutohedron https://hexnet.org/content/permutohedron Symmetry group of a regular hexagon <p>In this image we see the symmetry group D<sub>6</sub> of a regular hexagon. The hexagon can be rotated six ways, and reflected six ways. Note that any combination of two or more of these operations will still result in one of these twelve configurations.</p> Sun, 18 Apr 2010 04:16:43 +0000 https://hexnet.org/content/symmetry-group-regular-hexagon https://hexnet.org/content/symmetry-group-regular-hexagon An Introduction to Hexagonal Geometry <p><img src='/files/images/hexnet/p-6.png' title='Simple hexagon' alt='Simple hexagon' class='image-right'/> The following is a brief survey of some elemental properties of hexagons, and why they might be useful. It is not intended to be a comprehensive treatment of the subject. My specific concern here is with the mathematical properties of hexagons, and, to an extent, their role in the natural world. I have avoided discussing hexagons as they pertain to human culture, religion, history, and other "local" concerns, though there are many fascinating instances of hexagonality and sixness in these areas, and they will no doubt be treated more fully elsewhere at another time. </p> Fri, 16 Apr 2010 22:03:55 +0000 https://hexnet.org/content/hexagonal-geometry https://hexnet.org/content/hexagonal-geometry