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- Hypercube - Wikipedia
In geometry, a hypercube is an n -dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract
- Hypercube -- from Wolfram MathWorld
The hypercube is a generalization of a 3- cube to dimensions, also called an -cube or measure polytope It is a regular polytope with mutually perpendicular sides, and is therefore an orthotope It is denoted and has Schläfli symbol The following table summarizes the names of -dimensional hypercubes
- Hypercubes - Math is Fun
In Geometry we can have different dimensions The general idea of a cube in any dimension is called a hypercube, or n-cube Points, Lines, Surfaces, The magic binomial x+2 can tell us how many points, lines, surfaces etc for each dimension: (x+2) 0 = 1 For zero dimensions we have 1 point (x+2) 1 = x + 2 (x+2) 2 = (x+2) (x+2) = x2 + 4x + 4
- Hypercube - Polytope Wiki
Hypercubes are a direct generalization of squares and cubes to higher dimensions The n -dimensional hypercube, or simply the n -cube , has 2 n vertices, such that for every of n directions, half the vertices lie on one side, and half lie on the other
- Hypercube (Technical Notes) - Greg Egan
The animation above shows a packing of hyperspheres into hypercubes of dimensions ranging from 2 to 10; it is explained in more detail below Contents Counting the parts; Euler characteristic; Counting the symmetries; Classifying the rotations; The character table for the symmetries of the 4-cube; Metric properties; Packing with hyperspheres
- Hypercube Volume - Physics Insights
It has two hyperfaces on each axis; the hyperfaces are n -1 dimensional hypercubes In general, we call the volume enclosed by a hypercube an n-volume Ordinary "volume" (measured in things like quarts and liters) is 3-volume Area (measured in things like acres and square meters) is 2-volume
- Hypercube - Art of Problem Solving
As used in geometry, a hypercube is an extrapolation of the cube or square to n dimensions When n is not specified, it's generally assumed to be 4 For example, a 4th dimensional hypercube is called a tesseract Therefore, an n-dimensional hypercube is also known as an n-cube It is best drawn and represented in non-Euclidean geometry
- Hypercube: Definitions and Examples - Club Z! Tutoring
Among these intriguing constructs is the hypercube, a geometric figure that exists in higher dimensions With its perplexing properties and applications, the hypercube invites us to delve into the abstract world of multidimensional space
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