Go on, then. Why can't a polyhedron with many sides approximate a sphere?
He's using a polygon count limit approaching infinity to construct the sphere. The infinite 'corners', are the vertices of the polygons creating the sphere, and would parallel individual time lines extending from the beginning of time.
I think the confusion arose from implying that we needed a polyhedrons to
build an approximation of a sphere. I'm sure you meant the overall shape was a polyhedron, but actually
building the shape requires polygons.
We can at least say that a polyhedron is built up from different kinds of element or entity, each associated with a different number of dimensions:
Polyhedron: 3 dimensions - the body is bounded by the faces, and is usually the volume inside them.
Polygon: 2 dimensions - a face is a polygon bounded by a circuit of edges, and usually including the flat (plane) region inside the boundary. These polygonal faces together make up the polyhedral surface.
Edge: 1 dimension - An edge joins one vertex to another and one face to another, and is usually a line of some kind. The edges together make up the polyhedral skeleton.
Vertex: 0 dimensions - A vertex (plural vertices) is a corner point.
Nullity: -1 dimension - The nullity is a kind of non-entity required by abstract theories.Building a 3D model out of 3D components seems like an irrelevant tangent to the discussion, and also should not be asserting a fallacy in building it out of 2D components.