Math Art
Bipyramidal k-noid

Bipyramidal k-noid

Bipyramidal k-noid is a minimal surface, given by a Weierstrass representation, immersed.

Open Bipyramidal k-noid in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g
zm−smz⁢(−1+zm⁢sm)\frac{z^{m} - s^{m}}{z \left(-1 + z^{m} s^{m}\right)}
Height differential dh
(−1+(z⁢s)m)⁢(zm−sm)z⁢(−1+zm)2\frac{\left(-1 + \left(z s\right)^{m}\right) \left(z^{m} - s^{m}\right)}{z \left(-1 + z^{m}\right)^{2}}

Properties

Family
minimal
Given by
a Weierstrass representation
Curvature
zero mean curvature
Periodicity
not periodic
Ends
0
Embedding
immersed
Fidelity
exact
Exactness
numerical-integral

Definition

Extracted from the shipped row's source by AST (complete multi-line lambdas, g/dh lambdas) and reproduced numerically against the shipped callables over the complex plane, exactly -- no scalar slack.

Sources

Weierstrass data reproduced numerically against the shipped implementation (math_art/minsurf/zoo.py, row M3_BIPYR) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 0); dh: matches over 144 complex samples (worst 8.95e-16).