0
votes
1answer
49 views

why are these integrals equal?

I've been trying to analyse Steiner symmetrization. I've asked before about the symmetrization preserving $\textit{volume}$, I'm still going over the same proof. I think I understand a bit what is ...
1
vote
1answer
65 views

fundamental region for the rotational symmetry group of a tetrahedron

How would I find the fundamental region of a tetrahedron for its rotational symmetry group $\mathcal{T}$? I can think of how to find these regions in 2 dimensions, but I can't wrap my mind around the ...
4
votes
1answer
93 views

Magic theorem for cylinders? Symmetry classes according to Conway's notation?

My teacher Kirsi of Mat-1.3000 in Aalto University stated 17 symmetry classes for planes and 14 for spherical things (some lecture slides here). She used Conway Thurston's notation to classify ...
0
votes
1answer
117 views

How to find the matrix of reflection operator

I got a 3D space. In got a canonical equation of a plane: $ax + by + cz+ dt = 0$ How I can find the matrix of symmetric transformation transforming a point to its reflection?
0
votes
1answer
82 views

Polyhedra with symmetries order three

If I have a natural number $o=2n$ or $4n$ I can create a polyhedron whose group of symmetries has order $o$ by making a polygon like $C_n$ and then dragging it out to make a prism (I believe this is ...