Math Art
Schoen O,C-TO

Schoen O,C-TO

Schoen O,C-TO is a triply periodic minimal surface, defined as a nodal algebraic surface, immersed, with Pm-3m symmetry (a crystallographic space group).

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

Formula

0.6⁢(cos⁡(x)⁢cos⁡(y)+cos⁡(y)⁢cos⁡(z)+cos⁡(z)⁢cos⁡(x))−0.4⁢(cos⁡(x)+cos⁡(y)+cos⁡(z))+0.25=00.6 \left(\cos\left(x\right) \cos\left(y\right) + \cos\left(y\right) \cos\left(z\right) + \cos\left(z\right) \cos\left(x\right)\right) - 0.4 \left(\cos\left(x\right) + \cos\left(y\right) + \cos\left(z\right)\right) + 0.25 = 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
Pm-3m
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.