# Students' Work: Elliptic Linear Congruence

An elliptic linear congruence is a particular set of lines which sends precisely one line through each point of the three-dimensional real projective space. It is also called a regular spread. Our example admits - from a Euclidean point of view - a rotational symmetry.
This set of lines can be decomposed it into (i) reguli lying on a family of coaxial hyperboloids of revolution, (ii) the common axis of these hyperboloids, and (iii) the line at infinity of the plane that is perpendicular to the axis of revolution.
The image depicts some of these hyperboloids and the reguli on them.

Created by Mathias Neuwirth (2010) using POV-Ray - The Persistance of Vision Raytracer.

## Change Image

 37/249

Archimedean Solids
Cockles
Dupin Cyclides
Elliptic Linear Congruence
Geodesics on a Cone
Helices on a Helicoid
Hyperosculating Spheres
Impossible Objects
Klein Bottle
Knots
Menger Sponge
Möbius Tetrahedra
Pascal's Pyramid
Pipe Surfaces
Planar Sections of a Torus
Platonic Solids
Prince Rupert's Cube
Schwarz Lanterns
Snails
Spherical Loxodromes
Stationary Points
Striction Curves