Math Art
Fischer-Koch C(S)

Fischer-Koch C(S)

Fischer-Koch C(S) is a triply periodic minimal surface, defined as a nodal algebraic surface, immersed, with Ia-3d symmetry (a crystallographic space group).

Open Fischer-Koch C(S) in the interactive viewer →

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

Formula

cos⁡(2⁢x)+cos⁡(2⁢y)+cos⁡(2⁢z)+2⁢(sin⁡(3⁢x)⁢sin⁡(2⁢y)⁢cos⁡(z)+cos⁡(x)⁢sin⁡(3⁢y)⁢sin⁡(2⁢z)+sin⁡(2⁢x)⁢cos⁡(y)⁢sin⁡(3⁢z))+2⁢(sin⁡(2⁢x)⁢cos⁡(3⁢y)⁢sin⁡(z)+sin⁡(x)⁢sin⁡(2⁢y)⁢cos⁡(3⁢z)+cos⁡(3⁢x)⁢sin⁡(y)⁢sin⁡(2⁢z))=0\cos\left(2 x\right) + \cos\left(2 y\right) + \cos\left(2 z\right) + 2 \left(\sin\left(3 x\right) \sin\left(2 y\right) \cos\left(z\right) + \cos\left(x\right) \sin\left(3 y\right) \sin\left(2 z\right) + \sin\left(2 x\right) \cos\left(y\right) \sin\left(3 z\right)\right) + 2 \left(\sin\left(2 x\right) \cos\left(3 y\right) \sin\left(z\right) + \sin\left(x\right) \sin\left(2 y\right) \cos\left(3 z\right) + \cos\left(3 x\right) \sin\left(y\right) \sin\left(2 z\right)\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
Ia-3d
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.