Uploaded February 2013 | Updated September 2026, 2 weeks ago
The surface in this video has triangles connected under an angle of about 60 degrees, which leads to cycles of 10 triangles, yet also to spirals of 3, 8 or 9 triangles. The previous surfaces I found with spirals were in hyperbolic space, but this one is in regular space. From 3 angles it seems it may be Schwartz' P surface, but the holes in square formation are 45 degrees rotated compared to the P surface (at the end of this description a video-link explaining that this surface can be seen as the D or P surface anyway, yet from different angles). From 4 angles the surface looks like Schoen's GW surface, but that surface is built up in layers and has this hexagonal appearance only in 1 direction. Also, the units around the gaps in hexagonal formation are spiraling, which is not the case in the GW surface. I'm not sure if this is an approximation of a minimal surface, to me that seems possible because of the angle between touching triangles. In a flat surface where triangles are connected at the corners, this cannot be a minimal surface as all triangles will be absolutely flat. Triangles must be somewhat puffy in a minimal surface. The surface is not mentioned on the page on Triply Periodic Minimal Surfaces by Ken Brakke: http://www.susqu.edu/brakke/evolver/examples/periodic/periodic.html
In the following (unlisted) video I explain how to observe this surface as a skewed version of the D or P surface, meaning these surfaces have the same topology:
youtu.be/DoFrS_vqtFo
The surface in this video has triangles connected under an angle of about 60 degrees, which leads to cycles of 10 triangles, yet also to spirals of 3, 8 or 9 triangles. The previous surfaces I found with spirals were in hyperbolic space, but this one is in regular space. From 3 angles it seems it may be Schwartz' P surface, but the holes in square formation are 45 degrees rotated compared to the P surface (at the end of this description a video-link explaining that this surface can be seen as the D or P surface anyway, yet from different angles). From 4 angles the surface looks like Schoen's GW surface, but that surface is built up in layers and has this hexagonal appearance only in 1 direction. Also, the units around the gaps in hexagonal formation are spiraling, which is not the case in the GW surface. I'm not sure if this is an approximation of a minimal surface, to me that seems possible because of the angle between touching triangles. In a flat surface where triangles are connected at the corners, this cannot be a minimal surface as all triangles will be absolutely flat. Triangles must be somewhat puffy in a minimal surface. The surface is not mentioned on the page on Triply Periodic Minimal Surfaces by Ken Brakke: http://www.susqu.edu/brakke/evolver/examples/periodic/periodic.html
In the following (unlisted) video I explain how to observe this surface as a skewed version of the D or P surface, meaning these surfaces have the same topology:
youtu.be/DoFrS_vqtFo
