Pseudocrosscap
Pseudocrosscap
A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations
x(u,v) = (1-u^2)sinv
(1)
y(u,v) = (1-u^2)sin(2v)
(2)
z(u,v) = u.
(3)
See also
Cross-CapExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 337, 1997.Referenced on Wolfram|Alpha
PseudocrosscapCite this as:
Weisstein, Eric W. "Pseudocrosscap." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Pseudocrosscap.html