it's weird:

why did no one realize,
describe and apply the
exceptional topology,
maximum symmetry,
high complexity and
creative capabilities
of the unique object
'horn torus'
for centuries?
science ignored its existence completely
or neglected its relevance unduly
till this day ...

... really weird!

mathematicians, physicists and other scientists, please rectify this mysterious omission! - you should not relinquish such an important subject and object to the esoterics alone ...  invitation 
the horn torus is an excellent graphical representation of complex numbers, a compactification with considerable more properties than the Riemann sphere has, it connects zero and infinity in an amazing way, can be dynamised by two independent turns, rotation around the axis and revolution around the torus bulge, what creates an incredible complexity and forms a coherent comprehensive entity, also explaining the potential for self-interaction and fractal order of complex numbers, and finally - most important - horn tori can be interlaced into one another and so very well symbolise correlation between entities, easily interpretable as physical objects: 'space', 'time', 'particles', 'forces' ...
... and considered more generally: classical mathematics does not offer any well-elaborated and consistent theory of topological systems ('spaces') that are based on (respectively 'spanned' by) continuously and dynamically changing coordinates. Most practically working physicists doesn't bother that too much. They may be happy and content with their sophisticated software for computer simulations, animations and evaluations as explaining models for dynamic processes, being very successful thereby - no doubt, but from a more philosophical point of view that's not exactly the ideal solution for describing a dynamic physics. For true understanding we are in urgent need of revolutions (in thinking and as 'turns' :-), we should reflect on the topic more constructively, starting from a very basic level after having achieved full abstraction from our traditional imagination of (more or less static) spaces with embedded objects and processes by strict epistemological reduction to fundamental entities, and we have to aim at a - maybe disruptive - congruent mathematical model of physical 'reality' that comprises the pervasive and unstoppable dynamic as main intrinsic property.
Static doesn't occur in quantum reality, and no model works sufficiently without underlying dynamic. That's for sure!  → and here a  proposal for a related game

view explanatory video and this compilation