Apothem of a Regular Polygon

Is this method of constructing a regular polygon an approximation? or theoretically accurate?

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Halfing 3D Shapes

Cutting 3D shapes parallel to the base such that the top and bottom resulting portions have the same volume.

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Polygons in Polygrams

Each regular polygram has a regular polygon at its center.

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Cross Sections of Polyhedra

Cutting three dimensional shapes and looking at the possible shapes of the cross section.

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