# isothetic

A curve is isothetic if it consists entirely of lines parallel to one of the coordinate axes in a given rectilinear coordinate system. A polygon or polyhedron is isothetic if all of its edges are parallel to one of the coordinate axes.

An example of an isothetic polygon is the rectangle $\{(x,y):x_{1}\leq x\leq x_{2},\;y_{1}\leq y\leq y_{2}\}$ for some $x_{1}$, $x_{2}$, $y_{1}$, $y_{2}$. Examples of non-isothetic shapes are the tilted square $\{(x,y,z):|x|+|y|=1\}$ and the bipyramid $\{(x,y,z):|x|+|y|+|z|=1\}$.

(This entry is here because I couldn’t find a definition of isothetic on the web. If you know anything interesting about isothetic shapes, please adopt this entry!)

Title isothetic Isothetic 2013-03-22 15:54:33 2013-03-22 15:54:33 lha (3057) lha (3057) 8 lha (3057) Definition msc 52B11