Labs Sextic (35 cusps)
Labs Sextic (35 cusps) is an algebraic surface, defined by an implicit equation, immersed with singularities.
Open Labs Sextic (35 cusps) in the interactive viewer →
algebraic aperiodic def-implicit not-implemented singular tradition-classical
Properties
- Family
- algebraic
- Given by
- an implicit equation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed with singularities
- Fidelity
- exact
Definition
Degree-6 surface with 35 cusps, built Rohn-style as P - Q^3 = 0: P a product of six symmetrically chosen planes, Q a quadric with parameters (s,t,u,v). The family generically carries 30 cusps; the mirrored Singular script computes parameter values raising that to 35 and proves the count.
Not yet built
This surface is catalogued but not yet built by the extension, so it has no mesh or thumbnail here.
Sources
Not transcribed. The record exists to state that the surface is absent and why; a fabricated equation would be worse than a null.
- O. Labs, 'Algebraic Surface Homepage (announcing 'A Sextic with 35 Cusps')', The Algebraic Surface Homepage, algebraicsurface.net (Wayback rescue, captures to 2017-10-01; local mirror: algsurf/book/.../ch018_mainframe.md).
- O. Labs, 'A Sextic with 35 Cusps', Singular proof script sextic35cusps_all.sin (local mirror: algsurf/book/data/), which computes the parameters and proves ('theorem 1') that the surface has exactly 35 cusps and no other singularities. The script refers to an accompanying article for the family f_{s,t,u,v}.