Math Art
Fischer-Koch Y

Fischer-Koch Y

Fischer-Koch Y is a triply periodic minimal surface, defined as a nodal algebraic surface, immersed, with I4132 symmetry (a crystallographic space group).

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

Formula

cos⁡(x)⁢cos⁡(y)⁢cos⁡(z)+sin⁡(x)⁢sin⁡(y)⁢sin⁡(z)+sin⁡(2⁢x)⁢sin⁡(y)+sin⁡(2⁢y)⁢sin⁡(z)+sin⁡(x)⁢sin⁡(2⁢z)+cos⁡(x)⁢sin⁡(2⁢y)+cos⁡(y)⁢sin⁡(2⁢z)+sin⁡(2⁢x)⁢cos⁡(z)=0\cos\left(x\right) \cos\left(y\right) \cos\left(z\right) + \sin\left(x\right) \sin\left(y\right) \sin\left(z\right) + \sin\left(2 x\right) \sin\left(y\right) + \sin\left(2 y\right) \sin\left(z\right) + \sin\left(x\right) \sin\left(2 z\right) + \cos\left(x\right) \sin\left(2 y\right) + \cos\left(y\right) \sin\left(2 z\right) + \sin\left(2 x\right) \cos\left(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
I4132
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.