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 $\{(x,y):x_1\le x\le x_2,y_1\le y\le y_2\}$ 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
Canonical name	Isothetic
Date of creation	2013-03-22 15:54:33
Last modified on	2013-03-22 15:54:33
Owner	lha (3057)
Last modified by	lha (3057)
Numerical id	8
Author	lha (3057)
Entry type	Definition
Classification	msc 52B11