Lines on a Cubic Surface
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The level sets of the cubic polynomial 
. When 
, the surface contains six affine lines. When 
, the surface contains 24 affine lines. For each line, one coordinate is constant, so the lines can be grouped into three sets of eight (shown in different colors) depending upon which coordinate plane the lines are parallel to.
Contributed by: Ryan Hoban (The Experimental Geometry Lab at the University of Maryland) (March 2011)
Based on work by: William Goldman
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: 
, surface contains no affine lines
Snapshot 2: , surface contains six affine lines
Snapshot 3: 
, surface contains 24 affine lines
Snapshot 4: 
, the surface contains 24 affine lines. There are four Eckardt points where three of these lines simultaneously intersect.
Permanent Citation
Cross-Cap Surface and Variations
Ali Naeemi
Bour's Minimal Surface and Variations
Ali Naeemi
Boy Surface and Variations
Ali Naeemi
A Family of Surfaces Including a Möbius Strip
Ali Naeemi
Riemann Surface Transition
Michael Trott
Contours of Algebraic Surfaces
Yu-Sung Chang
Quadratic Surfaces
Stephen Wolfram
Steiner Surfaces
Enrique Zeleny
Special Rose Surfaces
Sonja Gorjanc (University of Zagreb)
Some Named Algebraic Surfaces
Enrique Zeleny
