The infamous problem of representing numbers with four 4’s appeared for the first time in 1881 in a London science journal. In 2001, a team of mathematicians from Harvey Mudd College found that we can even get four 4’s to approximate four notable constants: the number e, π, acceleration of gravity, and Avogadro’s number.
Take 6 points on a circle such that every second edge (green chords) has length equal to the radius of the circle. Then the midpoints of the other three sides of the cyclic hexagon form an equilateral triangle.
Read more: https://www.archimedes-lab.org/2-Sunday_puzzle_43.html
A 3D regular hexahedron solid (cube) passing through a 2D plane:
In geometry, the isogonic center (aka Fermat–Torricelli point) of a triangle, is a point such that the total distance from the three vertices of the triangle to the point is the minimum possible.