Hypocycloid prove that an epicycloid with "k" cusps moves snugly inside one with "k"+1 cusps. The evolute of a hypocycloid is an enlarged version of the hypocycloid itself, while the involute of a hypocycloid is a reduced copy of itself. The pedal of a hypocycloid with pole at the center of the hypocycloid is a rose curve. The isoptic of a hypocycloid is a hypocycloid. Curves similar to hypocyloids can be drawn with the Spirograph toy. Specifically, the Spirograph can draw hypotrochoids and epitrochoids. The Pittsburgh Steelers' logo, which is based on the Steelmark, includes three astroids (hypocycloids of four cusps).
Spacewarp (toy) Spacewarp (toy) Spacewarp is line of build-it-yourself, marble run toy "roller coasters" first made in the 1980s by Bandai. Users cut lengths of track to the correct size from a single roll of thick plastic tubing, forming curves and loops held in place by plastic track rail holders which attach to metal rods held vertical in a black plastic base. Steel balls roll around the track and on to a battery-powered Screw conveyor that takes them to the top to start all over again. Production of Spacewarp toys ended around 1988. Replacement parts were sold until 1995. A redesigned Spacewarp