Solid · Prisms and pyramids
Cube
Six equal square faces.
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Dimensions
Results
volume V
surface area S
space diagonal d
Formulas
Volume counts unit cubes: a layers of a by a. The space diagonal is Pythagoras twice.
Checked: the V, S formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
Topologically a ball. Its surface has V = 8 vertices, E = 12 edges and F = 6 faces, and V − E + F = 2, as for every convex polyhedron (Euler, 1758). More on the lens.