What is the highest percentage of surface area that can be seen at any given moment on a symmetrical object?
On a sphere its 50% right? (or close to it)
On a four-sided pyramid viewed from one of its points it would be 75%?
Can you get any higher?
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3What do you mean by symmetrical? The sphere has more symmetries than the tetrahedron. – Mark Bennet Oct 01 '19 at 21:06
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I wonder about higher dimensional spheres. Does the ratio stay 50%? – Charles Hudgins Oct 01 '19 at 21:23
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Oddly enough, this question is basically the same as this from a few years back. – Mark S. Oct 01 '19 at 21:39
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If a pyramid with a regular polygon base is symmetric enough for you it can be as close to $100\%$ as you like. Just make the altitude huge compared to the side of the base and look from above the point. You will see all the surface except the base.
Ross Millikan
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If we regard "symmetric enough" as condition that isometry group acts irreducibly, then question becomes quite interesting. – xsnl Oct 01 '19 at 22:43
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I thought about that aswell, and that is definetley one way to solve it. In the end i decided that such a shape wasn't symmetrical enough for me. Then again, what interessed me about the question was the open nature of it and i think there may be many ways to approach it. – Manfred Gunnarsson Oct 02 '19 at 18:45