Word-for-word translation: without change (from the Greek allagma: change).

A curve or surface is said to be anallagmatic if it is invariant under inversion.
All anallagmatic surfaces can be generated as cyclides, i.e. as the envelopes of spheres orthogonal to the inversion sphere (in the case of a positive power), the centers of which describe one of the deferents of the curve (in plural form, because there can indeed be several generations of this kind).

Examples of anallagmatic surfaces:
    - the cones (with respect to their vertex)
    - the sphere
    - the torus
    - more generally, the Dupin cyclides.
 
 

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© Robert FERRÉOL 2017