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While you consider my thoughts about oblique move-sections, here are some name ideas for pieces having only radial ones. Aanca was the name originally applied to what we call the Gryphon itself as the game for which that piece was invented (Grande Acedrex) was itself Spanish. As the Gryphon's winged nature suits a piece that ends up moving a Rook to reach the same destinations as the Flamingo and (on a big enough board) my own Ibis, perhaps a Wazir-then-Bishop should have a similarly appropriate name. In From Ungulates Outwards I suggest church titles for n+1:n leapers beyond Antelope - Rector, Parson, Curate, Deacon - so perhaps the piece should be an Archdeacon, not ranking far beow Bishops themselves. Gryphon+Archdeacon might then be Archgryphon. For Alfil-then-Rook (first destination as Zebra) I can think of the name Zephyr, something also flying through the sky but starting like Zebra, and for Dabbaba-then-Bishop (first destination as Camel) Lama, a Buddhist priestly title that is a homophone for the Camel's relative the Llama. I also have some name ideas for pieces using the cubic nonstandard diagonal (commonly called triagonal).