Honeycombs derived from the octahedral/tetrahedral honeycomb, Page 3

The four honeycombs described on the previous page, 10Y4-8T-n, 10Y4-8T-ortho, 10Y4-8T-meta and 10Y4-8T-para can also be elongated by the insertion of layers of triangular prisms between each layer of pyramids and tetrahedra.  The four equivalent honeycombs then become 5Y4-4T-6P3-tri-n5Y4-4T-6P3-tri-ortho, 5Y4-4T-6P3-tri-meta and 5Y4-4T-6P3-tri-para.  The insertion of the 'tri' in the name is to distinguish these from the previously discussed 5Y4-4T-6P3-sq-ortho and 5Y4-4T-6P3-sq-gyro formed from layers with square faces exposed.

The table below shows all four modes with the same colour coding as previously.





As on the previous page, the ortho and meta modes each have two forms, an alternating form where the gyrations of pi/3 or 2pi/3 respectively alternate back and forth, and a helical form where the gyrations continue in the same direction. (Discovered by Richard Klitzing, 2013).

Incidence matrices for all the above honeycombs are given by Richard Klitzing here.

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