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I was shocked to watch Anton Petrov's latest video, "Wow, Incredible Evidence That Universe Is Not Symmetric After All", where he says that the Tetrahedron is the simplest object that is not Z(2)-symmetric.

Does this mean that you can't connect four equilateral triangles to form a symmetric polyhedron, or is Anton wrong?

ty.

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Duce ex Machina
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    I don't have the time to look through that video, but surely a regular tetrahedron has reflections as symmetries. If you look at the animation to show its order two rotational symmetry you will see that it also has as a symmetry the reflection w.r.t. the plane intersecting the surrounding cube along the diagonal of the top face and perpendicular to it. – Jyrki Lahtonen Feb 11 '24 at 21:22
  • So Anton is wrong. that's what I thought. Sorry for asking a stupid question. – Duce ex Machina Feb 11 '24 at 21:26
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    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Feb 11 '24 at 21:32
  • OK, I withdraw the question, your honor. Does deleting a question have a negative impact on your number of points, or whatever you call it? Normally I wouldn't care, but as a brand new user, I don't yet have enough point to do some things. – Duce ex Machina Feb 11 '24 at 21:36
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    Saying that the tetrahedron is not $Z(2)$ symmetric can probably mean that the tetrahedron is not centrally symmetric, which is well known. – uniquesolution Feb 11 '24 at 22:11
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    There is no such a thing as the tetrahedron. Some tetrahedra are symmetric, some are not. – Moishe Kohan Feb 12 '24 at 01:16

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