Talk:Truncation (geometry)

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Uniform Polytopes (inactive)

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Analogies to quasitruncation for the other operations

Coxeter et al. (1954) in their famous paper on uniform polyhedra do indeed refer to what we could call quasicantellation and quasicantitruncation, although of course not under those names: they call them instead r'{^q
_r} and t'{^q
_r}, having called r{^q
_r} the rhombicuboctahedron-analogue instead of Norman Johnson's term the cantellation. Just like the quasitruncation t'{r, q}, these are defined with respect to the external rather than internal bisectors of the Schwarz triangle's angles, or in the case of the quasicantitruncation the excentre instead of the incentre. So we could mention these operations, which take the cube to the quasirhombicuboctahedron 3 4/3 | 2 and the quasitruncated cuboctahedron 2 3 4/3 | instead of the rhombicuboctrahedron 3 4 | 2 and the truncated cuboctahedron 2 3 4 |. Double sharp (talk) 15:53, 17 September 2018 (UTC)[reply]

Inverse operation

Is there a common terminology for the opposite of a truncation, namely the "drawing out" of faces until they become vertices? The images on the right show, that "untruncating" the dark faces of a disdyakis triacontahedron creates a (non-Catalan) pentagonal hexecontahedron. Watchduck (quack) 02:11, 25 October 2020 (UTC)[reply]