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The order complex. Generating Triply Periodic Minimal surface structures

, 2014
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Stability of triply periodic minimal surfaces

Differential Geometry and its Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ejiri, Norio, Shoda, Toshihiro
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Triply periodic minimal balance surfaces: a correction

Acta Crystallographica Section A Foundations of Crystallography, 1993
In previous papers, 15 families of minimal balance surfaces that can be generated with the aid of disc-like surface patches were noted. Recently, it has become apparent that the inherent symmetry of two of these families, the C(S) surfaces and the Y surfaces, is higher than the symmetry used for their generation.
E. Koch, W. Fischer
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New families of triply periodic minimal surfaces

Journal of the Chemical Society, Faraday Transactions, 1994
The established results regarding balanced minimal surfaces of orthorhombic symmetry are analysed and supplemented here. We commence by reviewing the simplest examples, possessing a genus value (per unit cell) of 3. From this foundation we construct a generalised approach, and apply it to the next simplest cases.
Andrew Fogden, Markus Haeberlein
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Design procedure for triply periodic minimal surface based biomimetic scaffolds

Journal of the Mechanical Behavior of Biomedical Materials, 2022
Cellular additively manufactured metallic structures for load-bearing scaffolds in the context of bone tissue engineering (BTE) have emerged as promising candidates. Due to many advantages in terms of morphology, stiffness, strength and permeability compared to conventional truss structures, lattices based on triply periodic minimal surfaces (TPMS ...
Fabian Günther, Markus Wagner, Stefan Pilz, Annett Gebert, Martina Zimmermann   +4 more
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On limits of triply periodic minimal surfaces

Annali di Matematica Pura ed Applicata (1923 -), 2018
A minimal surface in \(\mathbb{R}^3\) is said to be periodic if it is connected and invariant under a group \(\Gamma\) of isometries of \(\mathbb{R}^3\) that acts properly discontinuously and freely. This paper under review is focussed on the triply periodic case, i.e., \(\Gamma\) is chosen to be a rank-three lattice in \(\mathbb{R}^3\).
Norio Ejiri, Shoichi Fujimori, Toshihiro Shoda   +2 more
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On Triply Periodic Minimal Balance Surfaces

Structural Chemistry, 2002
A strategy for finding all triply periodic minimal balance surfaces (TPMBS) will be sketched mainly on the basis of fundamental domains of space group pairs of index 2. Some possibilities are confirmed, but there is no TPMBS for the space group pair Ia\({\bar 3}\)/Pa\({\bar 3}\), as formerly conjectured.
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Negatively curved graphite and triply periodic minimal surfaces

Journal of Mathematical Chemistry, 1994
The Weierstrass representation has been used to construct negatively curved graphite in which atoms rest no a perfect triply periodic minimal surface. By applying the Bonnet transformation on a patch of the D surface decorated with graphite we have been able to construct the Gyroid and P minimal surfaces.
H. Terrones, A. L. Mackay
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Triply periodic minimal surfaces decorated with curved graphite

Chemical Physics Letters, 1993
Abstract Hypothetical negatively curved structures derived from graphite are described, in which all carbon atoms rest on triply periodic minimal surfaces (TPMS). The D minimal surface was calculated using the Weierstrass representation. By applying the Bonnet transformation to the D surface, the gyroid and P surfaces were constructed.
Humbeto Terrones, Alan L. Mackay
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