Quadrapike (Sparkoid): A Formal Geometric Definition and Comparison with the Astroid

Despite its ubiquity in art, architecture, typography, and digital iconography, the planar figure formed by four mutually tangent quarter-circle arcs arranged inward has historically lacked a concise, standardized name in Euclidean geometry. Existing descriptions rely on cumbersome phrases such as "regular concave circular quadrilateral" or erroneously conflate the figure with the astroid (a four-cusped hypocycloid). This note formally introduces two complementary designations for this fundamental figure: Quadrapike (denoting its formal geometric structure of four sharp cusps) and Sparkoid (denoting its visual and design form). Key metric properties, construction methods, and a rigorous comparison with the classical astroid are presented.