,![\[
\sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \geq \frac{4(ab + bc + ca)}{\sqrt{(a + b)(b + c)(c + a)}}
\]](http://latex.artofproblemsolving.com/e/7/2/e72fd0f134289c359bc8766440babc52ae131961.png)
satisfied 
Find the minimum of 
Y by FaThEr-SqUiRrEl, Mango247
Let us consider polyhedrons that possess the following property: For any two vertices of such polyhedron it is possible to find a third vertex such that these three vertices together form an equilateral triangle.
The regular tetrahedron has this property. Are there any other polyhedrons like this?
(Bakaev E.V.)
The regular tetrahedron has this property. Are there any other polyhedrons like this?
(Bakaev E.V.)
This post has been edited 1 time. Last edited by parmenides51, Apr 20, 2021, 7:01 PM
