  Innocent musing on geodesics on the surface of helical pasta shapes leads to
a single continuous 4-parameter family of surfaces invariant under at least a
1-parameter symmetry group and which contains as various limits spheres, tori,
helical tubes, and cylinders, all useful for illustrating various aspects of
geometry in a visualizable setting that are important in special and general
relativity. In this family the most aesthetically pleasing surfaces come from
screw-rotating a plane cross-sectional curve perpendicular to itself, i.e.,
orthogonal to the tangent vector to a helix. If we impose instead this
orthogonality in the Lorentzian geometry of 3-dimensional Minkowski spacetime
with a timelike helical "central" world line representing a circular orbit, we
can model the Fermi Born rigid model of the classical electron in such an orbit
around the nucleus, and visualize the Fermi coordinate grid and its
intersection with the world tube of the equatorial circle of the spherical
surface of the electron (suppressing one spatial dimension). This leads what we
might playfully term "relativistic pasta". This is a useful 2-dimensional
stationary spacetime with closed spatial slices on which to illustrate the
slicing and threading splittings of general relativity relative to a Killing
congruence, like stationary axisymmetric spacetimes including the rotating
black hole family.
