differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

, the lidinoid is a triply periodic

minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

. The name comes from its Swedish discoverer Sven Lidin (who called it the HG surface). It has many similarities to the

gyroid A gyroid is an infinitely connected Triply periodic minimal surface, triply periodic minimal surface discovered by Alan Schoen in 1970. It arises naturally in polymer science and biology, as an interface with high surface area. History and pr ...

, and just as the gyroid is the unique embedded member of the

associate family In differential geometry, the associate family (or Bonnet family) of a minimal surface is a one-parameter family of minimal surfaces which share the same Weierstrass data. That is, if the surface has the representation :x_k(\zeta) = \Re \left\ ...

of the Schwarz P surface the lidinoid is the unique embedded member of the associate family of a Schwarz H surface. It belongs to

space group In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that ...

230(Ia3d). The Lidinoid can be approximated as a

level set In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value , that is: : L_c(f) = \left\~. When the number of independent variables is two, a level set is call ...

: :

+ 0.15 = 0 \end

References

External images

The lidinoid at the minimal surface archive

Minimal surfaces Differential geometry of surfaces {{differential-geometry-stub