how to do union operation over touching polyhedra

[Zhaiyu]

Dear members,

I'm trying to do boolean union operation over multiple touching polyhedra into one but couldn't find how to achieve this with Sage. For example, how can I merge these two cubes and dissolve the interior face (the touching face):

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# two cubes touching

cube_a = Polyhedron(vertices=[(0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1)])

cube_b = Polyhedron(vertices=[(1,1/2,0), (1,1/2,1), (1,3/2,0), (1,3/2,1), (2,1/2,0), (2,1/2,1), (2,3/2,0), (2,3/2,1)])

# visualize

cube_a.plot() + cube_b.plot()

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The polyhedra can be assumed all convex, and each touching pair share a polygon interface. I found polyhedron.intersection(other), but no polyhedron.union(other) or so. Any workaround I can do? Thanks in advance.

Best, Zhaiyu

[Dima Pasechnik]

The union will in general be non-convex, and Sage doesn't handle
non-convex polyhedra.
The best you can hope for is to construct the convex closure.

E.g. for polytopes (specified by vertices) just take the polytope spanned by the
union of the vertices.

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