Math Art
Lidinoid (nodal approximation)

Lidinoid (nodal approximation)

Lidinoid (nodal approximation) is a triply periodic minimal surface, defined as a nodal algebraic surface, genus 3 per unit cell, embedded, with Ia-3d symmetry (a crystallographic space group).

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chiral def-nodal embedded has-approximation implemented minimal minimal-periodic tradition-crystallographic triply-periodic

About

A triply periodic minimal surface of genus three found by Sven Lidin, and the gyroid's near relative: both are embedded members of associate families, arrived at by rotating a patch rather than by reflecting one. It stands in the same relation to the H surface as the gyroid does to Schwarz P.

Formula

0.5⁢(sin⁡(2⁢x)⁢cos⁡(y)⁢sin⁡(z)+sin⁡(2⁢y)⁢cos⁡(z)⁢sin⁡(x)+sin⁡(2⁢z)⁢cos⁡(x)⁢sin⁡(y)−cos⁡(2⁢x)⁢cos⁡(2⁢y)−cos⁡(2⁢y)⁢cos⁡(2⁢z)−cos⁡(2⁢z)⁢cos⁡(2⁢x))+0.15=00.5 \left(\sin\left(2 x\right) \cos\left(y\right) \sin\left(z\right) + \sin\left(2 y\right) \cos\left(z\right) \sin\left(x\right) + \sin\left(2 z\right) \cos\left(x\right) \sin\left(y\right) - \cos\left(2 x\right) \cos\left(2 y\right) - \cos\left(2 y\right) \cos\left(2 z\right) - \cos\left(2 z\right) \cos\left(2 x\right)\right) + 0.15 = 0

Properties

Family
minimal-periodic
Given by
a nodal algebraic surface
Curvature
zero mean curvature
Periodicity
triply periodic
Genus per cell
3
Ends
0
Embedding
embedded
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.