Editing Hexagram (section)

== Construction by linear algebra ==
[[File:Hexagram-cube.png|thumb]]
A regular hexagram can be constructed by [[orthographic projection|orthographically projecting]] any [[cube]] onto a plane through three vertices that are all adjacent to the same vertex.  The twelve midpoints to edges of the cube form a hexagram.  For example, consider the projection of the unit cube with vertices at the eight possible binary vectors in three dimensions <math>(1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1,1,1)</math> onto the plane <math>x+y+z=1</math>.  The midpoints are <math>(0,0,1/2),(0,1/2,1/2),(0,1,1/2),(1,1,1/2)</math>, and all points resulting from these by applying a permutation to their entries.  These 12 points project to a hexagram: six vertices around the outer hexagon and six on the inner.