Contents
Which figures can be formed by the intersection of a plane and a cube?
The intersection of a cube and a plane can be a triangle: but there’s no way to produce a circle, since none of a cube’s edges or faces is curved.
What is the intersection of a cube?
Whenever we cut the cube with a plane, each edge of the cross section corresponds to an intersection of one of the cube’s faces with the plane. Since the cube has only six faces, it is impossible to cut it with one plane and create an octagonal cross section.
What shape do you get if you cut a cube in half?
Yes we do: the regular octahedron, one of the five Platonic solids. That’s the intersection set we are looking for. If you hang a hy- percube by a vertex and cut it in half with a horizontal 3- dimensional hyperplane, the intersection set is an octahedron.
What happens when a plane intersects a 3-dimensional shape?
Some geometers are very interested what happens when a plane intersects or cuts a 3-Dimensional shape. Examine the GeoGebra workspace. The light blue rectangle represents, like a piece of paper, a small part of a plane cutting through rectangular prism — a cube.
What is the shape of a plane cutting a cube?
The magenta shape represents the polygon that would be formed if the plane actually cut the cube. Use the various sliders to experiment with different “slices” of the cube. Observe what polygons are created when a plane slices through a rectangular prism like a cube.
Can you make a triangle out of a cube?
You should be able to construct a square, a rectangle, a triangle and a trapezoid. Construct each of these polygons by slicing the cube with the plane. Copy an image of each to the clipboard and paste the image into a Word file. Print the Word file and add it to your Math Journal.
What kind of polygon is created when a plane slices through a cube?
Observe what polygons are created when a plane slices through a rectangular prism like a cube. What shapes did you observe? You should be able to construct a square, a rectangle, a triangle and a trapezoid. Construct each of these polygons by slicing the cube with the plane.