Cuboctahedral Quartic
Cuboctahedral Quartic is an algebraic surface, defined by an implicit equation, immersed, with Oh symmetry (a point group).
Open Cuboctahedral Quartic in the interactive viewer →
algebraic aperiodic def-implicit immersed implemented tradition-classical
Formula
Properties
- Family
- algebraic
- Given by
- an implicit equation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Symmetry
- Oh
- Symmetry kind
- point group
- 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 0).
- 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).
- E. Goursat, 'Etude des surfaces qui admettent tous les plans de symetrie d'un polyedre regulier', Ann. Sci. ENS 3e serie 4 (1887).