September 22, 2016 7:51am A two-dimensional square is composed of four edges and four vertices. A third-dimensional square is called a cube, and it is composed of six squares, twelve edges, and eight vertices. A fourth-dimensional cube is called a tesseract, and it is composed of eight cubes, twenty-four squares, thirty-two edges, and sixteen vertices. A fifth-dimensional tesseract is called a pentacube, and it is composed of ten tesseracts, forty cubes, eighty squares, eighty edges, and thirty-two vertices. A sixth-dimensional pentacube is called a dodecapeton, and it is composed of twelve pentacubes, sixty tesseracts, one hundred and sixty cubes, two hundred and forty squares, one hundred and ninety-two edges, and sixty-four vertices. A seventh-dimensional dodecapeton is called a hepteract, and it is composed of fourteen dodecapetons, eighty-four pentacubes, two hundred and eighty tesseracts, five hundred and sixty cubes, six hundred and seventy-two squares, four hundred and forty-eight edges, and one hundred and twenty-eight vertices.
