We introduce a natural partial order on the set Cones(d) of rational cones in R-d. The poset of normal polytopes, studied by Bruns and the authors (Discrete Comput. Geom. 56:1 (2016), 181-215), embeds into Cones(d) via the homogenization map. The order in Cones(d) is conjecturally the inclusion order. We prove this for d = 3 and show a stronger version of the connectivity of Cones(d) for all d. Topological aspects of the conjecture are also discussed.
- rational cone
- poset of cones
- geometric realization of a poset
- TORIC VARIETIES