Consider a convex polyhedra such that Euler's Polyhedra Formula applies...

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Consider the proposition of Euler that V - E + F = 2 for polyhedra. It is famously known that Euler's original proof failed to preserve convexity when considering the removal of vertices from polyhedra by means of removing pyramids from the polyhedra--to arrive at a simple tetrahedron.

Or, rather, that his process for the removal of vertices could lead to non-convex polyhedra, or even degenerate polyhedra. Provide an example using a hexagonal pyramid stacked onto a hexagonal prism where Euler's removal process creates a non-convex shape e.g. fails to preserve convexity. Give a detailed explanation.