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).
Maurice Denys (sheriff) Agnes Danvers, in the 4th. Q. The arms of Denys are: "Gules, three leopard's faces or jessant-de-lys azure, over all a bend engrailed of the last". The Denys arms blazoned with these tinctures survive earliest in British Library Add.MS 45131, f. 54, a 1509 drawing of Hugh Denys (d. 1511) at the deathbed of Henry VII. The armourials are the arms of Cantilupe of Candleston Castle, Glamorgan, probably granted as "arms of patronage" to their feudal officials or tenants the Denys's, differenced by the imposition of a bend engrailled, probably before 1258. Cantilupe arms, reversed for difference, are still borne