interpreting 4d representation of infinite dual

asked 2014-07-05 08:52:00 -0500

smbelcas gravatar image

updated 2015-01-14 03:52:17 -0500

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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