interpreting 4d representation of infinite dual

asked 10 years ago

smbelcas gravatar image

updated 10 years ago

FrédéricC gravatar image

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?

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