Quartic Symmetroid (pinned integer web)
Quartic Symmetroid (pinned integer web) is an algebraic surface, defined by an implicit equation, immersed.
Open Quartic Symmetroid (pinned integer web) in the interactive viewer →
algebraic aperiodic def-implicit immersed implemented tradition-classical
Properties
- Family
- algebraic
- Given by
- an implicit equation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- 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 (attribute shape). The shipped implementation in math_art/surfaces/algebraic.py is authoritative; an unverified transcription would silently define a different surface. The quartic determinant surface of a net of quadrics; ten nodes. 'The' symmetroid is a GENERIC construction, not a surface, so THE SHIPPED ROW PINS A MEMBER: det(x M0 + y M1 + z M2 + w M3) for four explicit integer symmetric matrices chosen by search for a node-rich real picture (printed in the module). Of the generic ten nodes this member shows SIX real ones, each verified by the self-test as det = grad det = 0 with the matrix rank EXACTLY 2 there; the other four are complex.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- E. W. Weisstein, "Peano Surface", "Chair", "Crossed Trough", "Handkerchief Surface", "Hunt's Surface", "Kiss Surface", "Menn's Surface", "Miter Surface", "Nordstrand's Weird Surface", "Tooth Surface", MathWorld -- A Wolfram Web Resource, mathworld.wolfram.com.
- T. Nordstrand, "Weird Cube" and the tooth/pillow object, per the MathWorld pages (Nordstrand 1997).
- G. Peano's 1899 counterexample; cf. the MathWorld page's history of the criterion it defeated.
- E. W. Weisstein, MathWorld, topic 'Algebraic Surfaces' -- the enumeration this absence was measured against.