horn torus entity
 

 
x = r·(1 − cos(ω2/2π))·cosω
y = r·(1 − cos(ω2/2π))· sinω
z = r · sin(ω2/2π)      

 
r = r1·2π / ω for r < r1
ω = 2π when r = r1 *)    
ω < 2π doesn't occur !  
 
ω is the toroidal horn
 torus angle,  r in the graphic above is not to scale
(increments of the single steps
 are pretty rough),
 depicted is the section
between 4 revolutions per 1 rotation  and 100 rotations per
 1 revolution
(for explanation click image)
 
 
 
*) r1 signifies the
standard dynamic horn torus, the 'μ-sterious'
mirror between
 'infinite outer world', consisting of electrons and photons, and the 'small inner world' of
hadrons and
 infinitesimal infinity.
 
Important note 1 in this context: the widely unknown infinitesimal infinity has the
 same cardinality as our known large universe (i.e. nuclei comprise whole universes).
 It's worth to think about that!
 
Note 2, equally imperative: horn torus depictions are allegoric only, their purpose is
 to symbolise mathematical particle properties - they don't occur as objects in
 our  familiar 3-dimensional space.
 
Dynamic variation of poloidal revolution and toroidal rotation, combined with
 alteration of size, can be expressed smartly by complex and hypercomplex numbers
 (quaternions, octonions, ...) - but
 
to describe the whole dynamics as abstract physical processes, including the
 interaction of intertwined nested horn tori, seems to be a task, which is
 not manageable by conventional
mathematics,