# Questions tagged [symmetry]

Questions about symmetry, in group theory, geometry or elsewhere in mathematics. See https://en.wikipedia.org/wiki/Symmetry

1,501 questions
Filter by
Sorted by
Tagged with
1 vote
37 views

### Find plane of symmetry (knowing reflection positions)

I have a set of 3 distincts points which I know the positions in 3D (say D1, D2, D3). I also know they are the plane-symmetry of 3 other distinct points in 3D (say B1, B2, B3) which I also know the ...
34 views

### Commutativity and symmetry of equalities

Is there any mathematical context, useful or not, in which a=b does not imply b=a? If yes and if it is useful please explain how.
110 views

### Generalised what?? CIrcle or line or ???..

What is the term for all objects that share the following property For any two different points in the shape the perpendicular bisector is an axis of symmetry of the shape. So for 2 dimensional ...
15 views

### Symmetry-invariant conservation laws using Multi-reduction [closed]

I am studying the article "Symmetry Multi-reduction Method for Partial Differential equations with Conservation Laws" by Anco and Gandarias and I am using Maple to code the examples in this ...
15 views

### How to perform Symmetrization?

Let $f:\mathbb{R}^n\to\mathbb{R}$ be an asymmetric function with respect to its variables. How can I transform it to become symmetric? For example, when $n=2$, take $f(x,y)=x+y^2$. Pairwise adding ...
1 vote
28 views

### Linear combination of tensor products of Pauli matrices that produce +/- paired eigenvalues

Eigenvalues of tensor products of Pauli matrices $\sigma_\mu\otimes\sigma_\nu (\mu,\nu\in\{x,y,z\})$ always come in pairs, as a consequence of the fact that eigenvalues of Pauli matrices are $\pm 1$. ...
20 views

### How many identical building blocks can make an icosahedrally symmetrical structure?

I'm working on an applied problem that requires designing symmetrical structures. I'd like to form an arrangement with full icosahedral symmetry (point group Ih in 3D) out of building blocks with Cs ...
127 views

### Symmetry group of rectangular cuboid

In this Wikipedia page it is said that the symmetry group of the rectangular cuboid (a box with three unequal dimensions) is a dihedral group $D_8$ (well, some people may call it $D_4$...) However, I ...
39 views

18 views

### Symmetric mollifier on cube instead of ball

It is known that there exists a symmetric, positive mollifier $\phi\in C^\infty_0(B_1(0))$, with $B_1(0)\subset\mathbb{R}^n$ the open unit ball. As far as I know, there also exists some positive ...
59 views

### Is there a finite group which is not the symmetry group of any n-space?

This is a natural follow-up to my previous question, here: A finite group that is not a symmetry group. An $n$-space symmetry is an isometry of $\mathbb{R}^n$. Given a subset $S$ of $\mathbb{R}^n$, ...