For centuries science ignored the existence of the geometric figure horn torus completely or
neglected its relevance unduly. Nearly nobody realized, described and applied the exceptional
topology, maximum symmetry, high complexity and creative capabilities of this unique object.
Now, in recent years, it increasingly appears in publications, mostly in context of particle and
quantum physics and in connection to cosmological questions. The subject is developing and
promises to stay exciting for a good while.
The static horn torus already shows pretty interesting properties, e.g. as replacement of the
Riemann sphere, but it becomes most thrilling when we add dynamic to the figure, when we
let it turn, around the main symmetry axis and around the torus bulge, when we let it change its
size during the turns, when we combine all these motions and when we finally interlace two, more
or even infinitely many such dynamic horn tori into one another, as roughly indicated in the image
above. Their 'unrolling' trajectories symbolise all occurences in one spatial
point.
A detailed description, combined with many animations, is provided on the link below. There the
horn torus model is presented as a kind of intellectual game, first to exercise imaginative
power, to improve abstract thinking and to generate lots of aha moments, then as proposal for a
different approach to physical questions, and finally as part of an interdisciplinary art project: