In geometry, an object exhibits symmetry if it looks the same after a transformation, such as reflection or rotation. Symmetry is important in art, math, biology and chemistry.

Researchers led by Prof. Xiaobei Zhang at Shanghai University (SHU), China, are interested in deformed Reuleaux-triangle resonator (RTR) which breaks rotational symmetry to simplify exceptional ...

An equilateral triangle has rotational symmetry of order 3. An equilateral triangle fits into its outline three times in a full 360° turn. Image caption, ...

In the mathematical sense, an object has rotational symmetry if there is an axis around which you can spin it so that at the end of a less-than-complete rotation, it looks just the same as it did ...

The symmetry group of a triangle, Galois realized, couldn’t be broken down any further, nor could that of a pentagon. But a 15-sided polygon is another story.

A deformed Reuleaux-triangle resonator is adopted to break rotational symmetry, where exceptional point for enhancing nanoparticle detection only needs one scatter to realize.

Now we can continue our analysis of the symmetries of a square. We know that one symmetry is “line reflection over the vertical line through the center”; another is “rotation about the ...

Rotational invariance is a symmetry exhibited by the circle: Rotate it any number of degrees and it looks the same. In the context of physical systems on the brink of phase changes, ...