Table of Contents
Introduction
Breaking up a Sphere
Moving Up a Dimension
Polyhedral Counterparts
Lower-Dimensional Cubes
Building Higher Dimensions
Into the Fourth Dimension
Sweeping Out a Cube
Sweeping Out a Hypercube
(*)
Counting Vertices
Counting Boundaries
Hypercube Faces
(*)
Sweeping Out Hypercube Faces
(*)
A Cube Unfolded
Folding a Cube
A Hypercube Unfolded
Folding a Hypercube
Perspective Views of Cubes
(*)
Rotating a Cube
Rotating a Hypercube
Solid Spheres and their Boundaries
Solid Cubes and their Boundaries
Cubes as Cross Products
Boundaries of Cross Products
The Boundary of a Square
The Boundary of a Cube
The Boundary of a Hypercube
A Square Cross a Solid Square
Tori in the Unfolded Hypercube
Linked Tori in the Hypercube
Torus in a Rotating Hypercube
The Smooth Analog
Smoothing the Hypercube
Projecting a Cube
Stereographic Projection
Stereographic Projection of a Band
Stereographic Projection From 4-Space
Two Infinite and Linked Solid Tori
Conclusion