So, in my usual way of throwing somewhat arbitrary commands at CASes to see what they do, I executed the following:
implex = Polyhedron(vertices = [[1.2,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]) implexdual = implex.polar() show(implexdual)
implex is a 3-simplex in 4-space.
implexdual is "A 4-dimensional polyhedron in RDF^4 defined as the convex hull of 4 vertices and 1 line."
Because it's 4-dimensional, I expected to see a wireframe Schlegel-diagram-ish thing when executing show(implexdual). What I get is four cones pointing in different directions, each of which has a smaller cone sticking out of its base.
Errrrrr.... what am I looking at?