# 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 |