This animation demonstrates various types of cuboids through everyday objects.
cuboid, square prism, cube, grouping of cuboids, set, grouping, mathematics
Grouping of cuboids
One way of grouping the cuboids is according to their formation.
A cuboid is a prism with a rectangular base.
Square prisms are a special type of cuboids.
Square prisms are cuboids with a square face. The face opposite to it is also a square. If there are no other square faces, the remaining 4 faces are congruent rectangles.
Cubes are a special type of square prisms, therefore they belong to a different category.
A cube is a cuboid with six square faces. Put differently, a cube is a square prism where the height and the length of the edge of the base are equal. Or, a cube is a cuboid with at least 3 square faces. If two of these are opposite to each other, we have a square prism, so the third face is a lateral face of the prism. In other words all the faces of the resulting prism are congruent squares.
If any two of the 3 faces are not opposite to a third, they share a common vertice. Being rectangles, all their opposite faces are congruent with them, so they are also squares.