Quaternions and spatial rotation around the "z" axis, then flip it 180 degrees around the "x" axis. Take the other book, flip it 180° around "x" axis first, and 90° clockwise around "z" later. The two books do not end up parallel. This shows that, in general, the composition of two different rotations around two distinct spatial axes will not commute. The vector cross product, used to define the axis–angle representation, does confer an orientation ("handedness") to space: in a three-dimensional vector space, the three vectors in the equation will always form a right-handed set (or a left-handed set, depending on how the cross
120-gon 120-gon In geometry, a 120-gon is a polygon with 120 sides. The sum of any 120-gon's interior angles is 21240 degrees. Alternative names include dodecacontagon and hecatonicosagon. A "regular 120-gon" is represented by Schläfli symbol {120} and also can be constructed as a truncated hexacontagon, t{60}, or a twice-truncated triacontagon, tt{30}, or a thrice-truncated pentadecagon, ttt{15}. One interior angle in a regular 120-gon is 177°, meaning that one exterior angle would be 3°. The area of a regular 120-gon is (with ) and its inradius is The circumradius of a regular 120-gon is This means that the trigonometric functions of