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 
.
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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.
- Kolmogorov-Smirnov Test
- Korselt's Criterion
- Kovalevskaya Exponent
- Kozyrev-Grinberg Theory
- k-Partite Graph
- Kramers Rate
- Krawtchouk Polynomial
- Kreisel Conjecture
- Kronecker Decomposition Theorem
- Kronecker Delta
- Kronecker Product
- Kronecker's Polynomial Theorem
- Kronecker Symbol
- Krull Dimension
- Kruskal's Algorithm
- Kruskal's Tree Theorem
- KS Entropy
- k-Statistic
- k-Subset
- k-Theory
- k-Tuple Conjecture
- Kuen Surface
- Kuhn-Tucker Theorem
- Kuiper Statistic
- Kulikowski's Theorem