Today (7th of July, 2018) marks 40 years of independence for the Solomon Islands.

To celebrate, I have decided to bake a cake! And what a pretty cake it's going to be:

• When viewed from the top, the cake will be shaped like a regular five pointed star, just like the ones on the Solomon Islands' flag.
• The sides will be perfectly vertical, the top (and bottom) perfectly horizontal
• To get the right colour, there'll be a thin layer of white frosting covering the top and the sides
• To top everything off, there's going to be a miniature flagpole with the flag of Solomon Islands standing smack in the middle of the cake.

Here's an early prototype (with star decorations instead of the flagpole) to give you the basic idea:

^{(Image source)}

Now then, as you probably knew (or at least guessed) already, the Solomon Islands were named after King Solomon, the undisputed champion of splitting stuff into equal parts.

Therefore, a proper plan for cutting the cake is definitely in order here:

1. Each piece should have an equal amount of cake.
2. There shouldn't be any cake left over.
3. Each piece should also have an equal amount of frosting.
4. I'm expecting to cut the cake into seven pieces, but it would be nice if the plan could account for other numbers of pieces too.
5. A most perfect plan would work even if I chose any other regular star as the cake's shape.

Can you help me come up with a cake cutting plan worthy of the occasion?

_{This is an adaptation of an age-old puzzle. I decorated it a little for the occasion; hopefully not too much to lose the beautiful point in the original.}