In the previous sections, you investigated cross sections and slices of 3-dimensional fiures, including prisms, cylinders, pyramids, cones, and cubes. In this section, you will investigate cross sections and slices of polyhedra, which are 3-dimensional figures that have all congruent faces. For example, a cube is a polyhedron because it has 6 faces that are all congruent squares.

Visit the link Platonic Solids-Slicing. This will open in a new browser tab or a new window.

In this sketch, the red line represents the plane creating the slice, and the view of the slice, or intersection, is shown in the window on the right. The slider beneath the polyhedron controls how far toward the front or the back the plane of intersection will be. You can change the orientation of the polyhedron by clicking and dragging on the blue polyhedron itself

Create a table like the one shown. You may create the table in your notes.

Journal Entry:

What are the limits on the types of slices that can be created from a given polyhedron? How do the shapes of the faces and the number of faces influence these limits?