Math Art
Complementary D

Complementary D

Complementary D is a triply periodic minimal surface, defined as a nodal algebraic surface, immersed, with a crystallographic space group.

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def-nodal has-approximation immersed implemented minimal minimal-periodic tradition-crystallographic triply-periodic

Formula

cos⁡(3⁢x+y)⁢cos⁡(z)−sin⁡(3⁢x−y)⁢sin⁡(z)+cos⁡(x+3⁢y)⁢cos⁡(z)+sin⁡(x−3⁢y)⁢sin⁡(z)+cos⁡(x−y)⁢cos⁡(3⁢z)−sin⁡(x+y)⁢sin⁡(3⁢z)=0\cos\left(3 x + y\right) \cos\left(z\right) - \sin\left(3 x - y\right) \sin\left(z\right) + \cos\left(x + 3 y\right) \cos\left(z\right) + \sin\left(x - 3 y\right) \sin\left(z\right) + \cos\left(x - y\right) \cos\left(3 z\right) - \sin\left(x + y\right) \sin\left(3 z\right) = 0

Properties

Family
minimal-periodic
Given by
a nodal algebraic surface
Curvature
zero mean curvature
Periodicity
triply periodic
Ends
0
Embedding
immersed
Orientable
yes
Symmetry kind
crystallographic space group
Fidelity
approximation

Definition

Standard nodal approximation as shipped in math_art/minsurf/tpms.py. No exact definition is stored for this surface, so this approximation is all the record has; `approximates` is null rather than pointing at itself.

Sources

Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.