CONCHOIDAL TRANSFORM OF SPACE

The conchoidal transformation of Euclidean space are defined. Under certain constraints, they form an Abelian group, and their composition acts on a single straight line or plane. The vertices of limaçons with a common base lie on the straight line and the cissoid of Diocles, and the inflection points on a generalized piriform quartic. The composition of conchoidal transformations of the plane forms seven families of congruent triangles, or two limaçons with one base circle form two families of congruent parallelograms. Under certain constraints, the composition of conchoid transformations of space is a conchoid transformation, and conchoid transformations can form a non-Abelian group.