Taubin Heart

Taubin Heart is an algebraic surface, defined by an implicit equation, immersed.

Open Taubin Heart in the interactive viewer →

algebraic aperiodic def-implicit immersed implemented tradition-classical

Formula

\left(x^{2} + \frac{9}{4} y^{2} + z^{2} - 1\right)^{3} - x^{2} z^{3} - \frac{9}{80} y^{2} z^{3} = 0

Properties

Family: algebraic
Given by: an implicit equation
Curvature: no condition imposed
Periodicity: not periodic
Ends: 0
Embedding: immersed
Fidelity: exact
Exactness: elementary

Sources

Closed form reproduced numerically against the shipped implementation (math_art/surfaces/algebraic.py) over 240 sample points: matches oracle x 1 over 240 points (worst 1.42e-13).

A. Cayley, "A Memoir on Cubic Surfaces", Phil. Trans. 159, 1869.
A. Clebsch, "Ueber die Flachen vierter Ordnung...", Journal fur die reine und angewandte Mathematik 69, 1868 -- the diagonal surface.
W. Barth, "Two projective surfaces with many nodes admitting the symmetries of the icosahedron", J. Algebraic Geometry 5, 1996.
H. Hauser, "Bildergalerie algebraischer Flaechen", Universitaet Wien -- the named gallery surfaces in the _HAUSER block below.
St. Endrass, "A Projective Surface of Degree Eight with 168 Nodes", J. Algebraic Geom. 6 (1997) 325-334 -- also the source of the five-parameter D8 x Z2 octic family; the 160- and 165-nodal parameter values are published on O. Labs's Algebraic Surface
Homepage, algebraicsurface.net (octics pages).