1. What is the standard n dimensional unit cube?
Vertices: Points (e1,e2,…,en) where each ei is either 0 or 1.
Edges: The line segments connecting vertices that are a distance 1 away from of each other (i.e. differ in one entry).

2. 4 Cube Vertices and Edges

3. 5 Cube Vertices and Edges)

4. Questions…
How many vertices are in the standard n dimensional unit cube?
How many edges are in the standard n dimensional unit cube?

5. General Strategy for Sketching an n Dimensional Cube
Create the vertices.
Create an orthonormal basis for the view plane. These vectors will determine the coordinate axes in the view plane.
Create the coordinates for the projected vertices (in the view plane).
Determine the connection order.
Sketch the edges by connecting the appropriate points in the view plane.

6. A Convenient View Plane

7. 4 Dimensional Cube
The sketch below shows the standard 4 dimensional unit cube using orthogonal projection onto the convenient view plane. The slides that follow show 5, 6, 7 and 8.

8. 5 Dimensional Cube

9. 6 Dimensional Cube

10. 7 Dimensional Cube

11. 8 Dimensional Cube