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Saddle polyhedra have contoured saddle-shaped faces that allow for interesting 3D tilings. This collection contains a sample of saddle polyhedra that are interesting and well suited for 3D printing. It is not a complete set, and I would be happy to post links to others that are posted.
There doesn’t seem to be a lot of agreement on naming saddle polyhedra. The names used here are not necessarily the “official” ones, but you can dig a bit deeper with the links provided.
Adamantane: This four-sided shape is derived from the diamond net. It can also be formed by starting with a rhombic dodecahedron, selecting four triads of faces that share a vertex, and forming a saddle from the skew hexagon that bounds the triads. (http://rcsr.net/polyhedra/ada)
Double Adamantane: Two adamantane units stuck together. You can also make a saddle polyhedron by cutting an adamantane in half.
Rhombic Dodecahedron Cluster: Related to the adamantane polyhedral. Formed by starting with a cluster of four rhombic dodecahedrons and creating saddles from the skew octagons made up of adjacent faces.
Expanded octahedron: This eight-sided shape is derived from the NbO cage. Six skew hexagons form the eight saddle faces. (http://rcsr.net/nets/nbo)
Body Centered Cubic: This shape is derived from the body centered cubic network. (http://rcsr.net/nets/bcu)
Wurtzite: The Wurtzite network forms two saddle polyhedra that are named here as “Wurtzite Small” and “Wurtzite Large.” 3D tilings are achieved by using the shapes separately or in the “Wurtzite Combined” form. (http://rcsr.net/nets/lon-b)
Williams W2: This shape is derived from the Williams W2 network. (http://rcsr.net/nets/isq)
Helpful resources:
Reticular Chemistry Structure Resource: http://rcsr.net/
Reflections concerning triply-periodic minimal surfaces: https://royalsocietypublishing.org/doi/full/10.1098/rsfs.2012.0023
Nets and Tiling: http://yaghi.berkeley.edu/research-news/MOK-tiling.pdf
Parallelohedra and topological transitions in cellular structures: https://www.researchgate.net/publication/233233020_Parallelohedra_and_topological_transitions_in_cellular_structures
