Calculations at an anticube. An anticube is a square uniform antiprism, or a cube with one side twisted for 45 degrees.
Enter the edge length and choose the number of decimal places. Then click Calculate.
Formulas:
Length and height have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
The anticube is a regular or uniform antiprism, meaning all its edges are of equal length, not only those of the square bases, but also those of the slanted sides. Like the cube, it has eight vertices. However, the number of edges and faces is higher. The anticube has 16 edges and 10 faces, because the number of edges and faces doubles in the direction of twisting, while remaining constant at the bases. In contrast, the cube has 12 edges and 6 faces, with four in the direction of the anticube's twisting, meaning the anticube gains four additional ones of each type, as each original edge and face effectively splits into two.
Depending on the counting method, the anticube is either the second or third shape in the infinite series of uniform antiprisms. The digonal antiprism is also known as degenerate antiprism and takes the form of a tetrahedron. The next shape, the uniform equilateral triangular antiprism, is the octahedron. Both the tetrahedron and the octahedron are Platonic solids, possessing a higher degree of regularity than the other antiprisms. The series continues by increasing the number of vertices at the base. Following the anticube comes the uniform pentagonal antiprism, and so on. The anticube holds a special place in this series, as it is the first of these shapes that is not a Platonic solid and is arguably used more frequently than the subsequent ones. Certain molecules, such as S8, exhibit this shape.
Stretching or compressing uniform antiprisms yields isosceles antiprisms. This can, of course, also be done with the anticube. One World Trade Center in New York features a shape similar to the isosceles square antiprism, or elongated anticube, though it tapers towards the top for structural reasons.