Labs Dodecic (132 A5 points)
Labs Dodecic (132 A5 points) is an algebraic surface, defined by an implicit equation, immersed with singularities.
Open Labs Dodecic (132 A5 points) in the interactive viewer →
algebraic aperiodic def-implicit 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
- Exactness
- elementary
Definition
Polynomial not stored: no closed form is stored for this surface, and its implementation could not be read back as one expression (constant 1j). The shipped implementation in math_art/surfaces/algebraic.py is authoritative; an unverified transcription would silently define a different surface. Part of a series of surfaces in P^3 with many A_j singularities (the page gives the count 12*11 = 132 for j = 5 but not the degree).
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- O. Labs, "A Sextic with 35 Cusps", arXiv:math/0502520 (2005) -- the D5 family (1) and Theorem 3, the real member with 30 cusps and 10 nodes shipped here.
- O. Labs, "Dessins d'Enfants and Hypersurfaces with Many A_j-Singularities", J. London Math. Soc. (2) 74 (2006) 607-622; arXiv:math/0505022 -- construction (4), the folding-polynomial critical counts, Theorem 7 and the 132 = 12*11 row of Table 1.
- O. Labs, Algebraic Surface Homepage, algebraicsurface.net, advent calendar 2002 Nos. 1 and 17 -- the descriptions the dodecic and Hyde rows are verified against. Mirrored locally under references/websites/algsurf/.
- S. V. Chmutov, "Examples of Projective Surfaces with Many Singularities", J. Algebraic Geom. 1 (1992) 191-196 -- the nodal construction the A_j series modifies.
- E. W. Hyde, "On a Surface of the Sixth Order Which Is Touched by the Axes of All Screws Reciprocal to Three Given Screws", Ann. of Math. (2) 2 (1901) 179-188 -- the surface the HYDE row rebuilds from its classical definition.
- R. S. Ball, "A Treatise on the Theory of Screws", Cambridge University Press (1900) -- the pitch quadric and the canonical form of a three-system used in the derivation.
- O. Labs, 'Advent calendar 2002, No. 1', The Algebraic Surface Homepage, algebraicsurface.net (Wayback rescue, captures to 2017-10-01; local mirror: algsurf/book/.../ch019_no_01.md).
- O. Labs, 'Dessins d'Enfants and Hypersurfaces with Many A_j-Singularities', J. London Math. Soc. 74 (2006) 607-622; arXiv:math/0505022 (converted, research/papers/algebraic-surfaces).
- Cover image of the SuSE Linux 8.1 distribution, per the page (Labs made the SuSE cover surfaces from version 7.1 on).