# Shape: Regular

## Regular

### Meaning

In mathematics, *regular* is a technical term. Regular can be used to describe either polygons or polyhedra. A regular polygon is a polygon that is both equilateral and equiangular. That is, a regular polygon is one whose sides each have the same length and whose angles each have the same measure. A regular polyhedron is a polyhedron whose faces are congruent regular polygons and whose polyhedral angles are congruent.

## Mathematical background

Students often miss the technical meaning of regular and substitute the every-day meaning of regular. Until they learn otherwise through examples, students interpret 'regular' as 'typical', 'ordinary', or 'average'. Hence, when asked to sketch regular polygons, students often sketch a variety of rectangles, those that are most 'typical' in thier experience. Some examples are regular in the mathematical sense (the squares), but other are not. Moreover, students rarely sketch examples of regular polygons with more than four sides. To many students, *regular pentagon* is an oxymoron -- there is nothing 'ordinary' about such a 'weird' shape!

## Etymology

## Related mathematical terms

Equilateral, Equiangular, Square, Polygon