Abstract
A cusphere, portmanteau of cube and sphere, is the constant magnitude surface in imaginary scator algebra. The computer renderings exhibit a fascinating geometry with great aesthetic value. The scator space in 1 + 2 dimensions, is endowed with a scalar (real) and two hyperimaginary components that can be represented in the three orthogonal axes of Euclidean space. A myriad of plane curves are obtained on the cusphere surface: Families of ellipses, circles and lemniscatae are three of the familiar ones. There are also less conventional ones, like four pointed stars and squircles. Implicit as well as parametric equations of these curves are derived. The three dimensional geometrical object is explored from different perspectives.
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