Kuutiokulmaprisma

Kuutiokulmaprisma is a hypothetical geometric solid used in geometry education to illustrate how combining basic solids can affect volume, surface area, and symmetry. The simplest form, often used in classroom exercises, is a cube of side length s with a square prism of height h attached to one of its faces along the full face.

Construction is straightforward: a square prism with base a square of side s is joined to the cube on one of the cube’s faces, sharing that face completely. The resulting solid extends from -s/2 to s/2 + h along the axis perpendicular to the shared face.

The volume of this composite solid is V = s^3 + s^2 h. The exterior surface area is SA = 6 s^2 + 4 s h, since the attached face disappears from the outer surface while the prism contributes four side faces of area s h and the prism’s far end face of area s^2.

The centroid lies on the attachment axis. With uniform density, the center of mass is located at a distance h/2 from the cube’s center along the attachment axis, a result that depends only on h and not on s.

Variations include using a rectangular prism or attaching to a different cube face, which changes the symmetry and dimensions. Kuutiokulmaprisma thus encompasses a family of shapes and provides a clear teaching example for composite solids, volume and surface area calculations, and centroid estimation.