Since he described symmetry in terms of rotations, I would expect that the object labeled (g) in the first figure would be symmetric under 360 degrees rotation. He says it's not symmetric.
A bit of background: Every object has a "group of symmetries". The smallest and easiest groups are those groups which contain only a single element, in case of symmetry groups the trivial identity symmetry. All those one-element groups are also referred to as "the trivial group". By abuse of language, we sometimes say that a object has "no" symmetries if it only has the trivial one.
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Since he described symmetry in terms of rotations, I would expect that the object labeled (g) in the first figure would be symmetric under 360 degrees rotation. He says it's not symmetric.
I suppose it's a shorthand for "no symmetries other than the trivial identity symmetry"?
Yes, that's indeed the case.
A bit of background: Every object has a "group of symmetries". The smallest and easiest groups are those groups which contain only a single element, in case of symmetry groups the trivial identity symmetry. All those one-element groups are also referred to as "the trivial group". By abuse of language, we sometimes say that a object has "no" symmetries if it only has the trivial one.