Hypercube

The generalization of a 3-Cube to -D, also called a Measure Polytope. It is a regular Polytopewith mutually Perpendicular sides, and is therefore an Orthotope. It is denoted and hasSchläfli Symbol . The number of -cubescontained in an -cube can be found from the Coefficients of .

The 1-hypercube is a Line Segment, the 2-hypercube is the Square, and the 3-hypercube is the Cube. Thehypercube in , called a Tesseract, has the Schläfli Symbol andVertices . The above figures show two visualizations of theTesseract. The figure on the left is a projection of the Tesseract in 3-space (Gardner 1977), and the figure onthe right is the Graph of the Tesseract symmetrically projected into the Plane(Coxeter 1973). A Tesseract has 16 Vertices, 32 Edges,24 Squares, and eight Cubes.

References

Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, p. 123, 1973.

Gardner, M. ``Hypercubes.'' Ch. 4 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American. New York: Vintage Books, 1977.

Geometry Center. ``The Tesseract (or Hypercube).'' http://www.geom.umn.edu/docs/outreach/4-cube/.

Pappas, T. ``How Many Dimensions are There?'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 204-205, 1989.

• Tractrix Evolute
• Tractrix Radial Curve
• Tractroid
• Transcendental Curve
• Transcendental Equation
• Transcendental Function
• Transcendental Number
• Transcritical Bifurcation
• Transfer Function
• Convergent Sequence
• Convergent Series
• Conversion Period
• Convex
• Convex Function
• Convex Hull
• Convex Optimization Theory
• Convex Polygon
• Convex Polyhedron
• Convolution
• Convolution Theorem
• Conway-Alexander Polynomial
• Conway Groups
• Conway Notation
• Conway Polyhedron Notation
• Conway Polynomial