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https://media.mathstodon.xyz/media_attachments/files/112/858/482/631/455/305/original/ed403398ddc0dc0c.jpg
The square pencils fit in the existing orthogonal channels through the gyroid, while the hexagonal ones have holes cut for them and pass through the vertices of the 2 laves graphs which are the skeletons of the surface (as shown here https://vimeo.com/2553639)
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