Clebsch Cubic Explorer — drag to orbit, scroll to zoom, right‑drag to pan.
Surface: 81(x³+y³+z³) − 189(x²(y+z)+y²(z+x)+z²(x+y)) + 54xyz + 126(xy+yz+zx) − 9(x²+y²+z²) − 9(x+y+z) + 1 = 0
Clebsch Cubic — Equations & Incidence
Projective form: \(x^3+y^3+z^3+w^3=(x+y+z+w)^3\)
Affine chart used in the renderer (\(w=1\)):
\(81(x^3+y^3+z^3) - 189(x^2(y+z)+y^2(z+x)+z^2(x+y)) + 54xyz + 126(xy+yz+zx) - 9(x^2+y^2+z^2) - 9(x+y+z) + 1=0\)
27 lines (parametrizations)
Tritangent planes
Each item lists the triple of line indices \(\{\ell_i,\ell_j,\ell_k\}\) lying in the plane.