K. Sugihara is a mathematical engineer that has devised a number of astonishing 3D illusions. A family of them consists in objects that change shape when reflected in a mirror. The effect needs to keep a fixed point of view, otherwise you see the "trick", and then it is a perfect material to be displayed with photos or to be recorded with a steady camera. No wonder that videos like this have become viral.
The mathematical explanation is surprisingly simple. Essentially a mirror behaves as another observer with a different point of view. If we do not move, we see a 3D curve on a plane and the whole trick is to construct a curve with quite different plane projections along two different directions. If the projection is a simple familiar curve like a circle or a square, we tend to identify the curve with it instead of guessing a more involved twisted curve in the space. See this paper for the details worked out in one example.
This is a paper folding template to construct a fake square prism that becomes a triangular prism through the mirror and vice versa.
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It is adapted from the page of D. Richeson, the author of the aforementioned paper and of other pieces on this topic. I have clipped the bottom part and added a tab because in this way the object stands by itself, without using hands, and one can use glue instead of adhesive tape. The latter does not ease the folding.
These are some photos of the result I have got with the template. The last one is still the same object after a rotation. By some reason the square reflected as a triangle is more perfect than the triangle reflected as a square.
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The result is quite good taking into account the thickness and rigidity of a sheet of paper as well as the clumsiness of the author.