My sorted posts, answers, comments in MEDIUM, the platform, on perfect numbers, and on tetrahedrons, icosahedrons, and cubes that indwell perfect numbers
Perfect numbers are exactly filled up, and filled in, by equal sized tetrahedrons, which are pyramids. Perfect numbers are also filled in by cubes. Take 496 for example, a perfect number. If you have 496 tetrahedrons, they are altogether made of 1992 triangles (1600+360+32). 496 tetrahedrons also make 24, 20-component icosahedrons, with 16 additional tetrahedrons. In cubes, 496 is the sum of the first several odd-edged cubes. One(1) cube plus(+) 27 cubes(3×9 cubes) plus(+) 125 cubes(5×25 cubes) plus(+)343 cubes(7×49 cubes). 1+27+125+343=496. These internal perfect cubes(1,27,125,343), viewed as components of perfect numbers, added together and sumed, are the perfect number 496. And not just 496, but this is true of all perfect numbers, that, internally, they are sets of perfect cube-clusteres, clustered together into perfect cubes, if you can see them that way. Whether tetrahedrons or cubes, they pack tightly. Each tetrahedron is made of four equilateral triangle...