Editing Astroid (section)

==Properties==
The astroid has four cusp singularities in the real plane, the points on the star. It has two more complex cusp singularities at infinity, and four complex double points, for a total of ten singularities.

The [[dual curve]] to the astroid is the [[cruciform curve]] with equation <math display="inline"> x^2 y^2 = x^2 + y^2.</math>
The [[evolute]] of an astroid is an astroid twice as large.

The astroid has only one tangent line in each oriented direction, making it an example of a [[hedgehog (geometry)|hedgehog]].<ref>{{cite journal
 | last1 = Nishimura | first1 = Takashi
 | last2 = Sakemi | first2 = Yu
 | doi = 10.14492/hokmj/1319595861
 | issue = 3
 | journal = Hokkaido Mathematical Journal
 | mr = 2883496
 | pages = 361–373
 | title = View from inside
 | volume = 40
 | year = 2011| doi-access = free
 }}</ref>