Sextic curves

thumb|Astroid thumb|The hypocycloid construction of the astroid. thumb|Astroid as the common Envelope (mathematics)|envelope of a family of [[ellipses of equation , where .]] [[File:sliding_ladder_in_astroid.svg|thumb|link=|The envelope of a ladder (coloured lines in the top-right quadrant) sliding down a vertical wall, and its reflections (other quadrants) is an astroid. The midpoints trace out a circle while other points trace out ellipses similar to the previous figure. [ ] hover over a ladder to highlight it.]] thumb|right|Astroid as an evolute of ellipse

thumb|Nephroid: definition

thumb|Rotated quadrifolium thumb|Quadrifolium created with gears

algebraic curve

algebraic curve