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If I load the Heptagrammic Cuploid in polyhedron view I see a bowl with seven sides, each side with 5 faces, and a regular heptagon as its base.

If I display the Folding Net view the base is not rendered on the screen but the rest is. I have not hidden or unhidden any face. There is no net for the base of the bowl. The info panel tells me the object has 35 facelets. It seems to me the side's (7 * 5 = 35) faces comprise the polyhedron but the heptagonal base is not part of it, ie the model has a heptagonal hole in the middle.

1) Why is the base not considered part of the polyhedron?

2) Why does the base render in one view but not the other?

Part of the base shows, but the central region is missing. This is because there's no enclosed volume above or below it. Nets are based on active stellation cells, and in this case there's no stellation cell above or below, so that part of the face is missing from the nets. It's not ideal, but you can just print the heptagram part another way, eg create a heptagrammatic prism of matching size and ju st print the heptagram.

Thanks for the quick reply.

Re printing the net for the heptagonal base; the method you give would be fine for a paper model where dihedral angles are not important as you can bend score-lines or tabs to suit when forming edges.

I want to make it out of timber so I will take the dimensions and dihedral angles of the heptagon from the edges of the side panels adjoining it. Each of the seven panels will be solid timber rather than being built of 5 faces. The heptagonal base will need to be made thicker than the mathematical model or (as you point out) the base will have zero thickness. Similarly the 7 side panels will be somewhat thicker too as otherwise there would be zero thickness where each has a coincident edge with its neighbours. I haven't got any glue that holds that kind of joint!