What is a hypercube and how do you understand a hypercube?

Tesseract, hypercube is also known as hypercube or octat, in geometry the quadruple cube is a four-dimensional analogy of the cube, the quadruple cube is to the cube, just like the cube is to the square, the quadruple cube is the four-dimensional convex polycyte, there are 8 cube cells, the cube dimension greater than 3 is the hypercube or the measurement polycell.

The standard tetracube in a four-dimensional Euclidean space is a convex hull of points (1, 1, 1, 1). It contains points: The four-dimensional cube is surrounded by eight hyperplanes (xi = 1).

Two pairs of non-parallel hyperplanes intersect to form a total of 24 square faces of a tetracube. Each edge has 3 cubes and 3 squares intersected. At each vertex there are 4 cubes, 6 squares, and 4 edges intersecting.

The four-dimensional cube has a total of 8 cubes, 24 squares, 32 edges, and 16 vertices. Each vertex of the cube is adjacent to 4 edges, so the vertex shape of the cube is a tetrahedron. So the Schlevley symbol for the tetrad is:

Its dual polysomal is a regular hexadecyte and the Schlevley symbol is. In popular understanding, it is to fold eight cubes in four-dimensional space to form a supercube, just as six squares are folded in three-dimensional space to form a cube. Projection A four-dimensional cube is not easy to imagine, but it can be projected into 3D or 2D space.

Hypercube, in geometry the four-dimensional cube is the four-dimensional analogy of the cube, the four-dimensional cube is to the cube, just like the cube is to the square, the four-dimensional cube is the simple old four-dimensional convex polycell, there are 8 cube cells, the cube dimension greater than 3 is the promotion of the hypercube or the measure polycell.

The hypercube, also known as the regular octat, cube column, 4-4 sided column, is a geometric product in a four-dimensional space.

Brief description: 1. The hypercube has no concept of 2-dimensional distance and angular wisdom;

2. It takes the same amount of time for any vertex in the hypercube to reach adjacent vertices at a constant velocity.

A zero-dimensional point that contains a zero-dimensional element (point).

A line segment in a single dimension, containing one one-dimensional element (a line segment) and two zero-dimensional elements (endpoints).

A two-dimensional square containing one two-dimensional element (polygon), four one-dimensional elements (edges), and four zero-dimensional elements (vertices).

A three-dimensional cube containing one three-dimensional element (three-dimensional), six two-dimensional elements (faces), twelve one-dimensional elements (edges), and eight zero-dimensional elements (vertices).

Compare the following equations:

x+2)^0=1

x+2)^1=x+2

x+2)^2=x²+4x+4

x+2)^3=x^3+6x^2+12x+8

It can be concluded that the number of k-dimensional elements contained in an n-cube is equal to the k-term coefficient of (x+2) n.

x+2)^4=x^4+8x^3+24x^2+32x+16

It can be concluded that the hypercube has 8 cubes (cells), 24 faces, 32 line segments, and 16 points.

This helps us to confirm the construction of the four-dimensional hypercube.

Hypercube, in geometry the four-dimensional cube is the four-dimensional analogy of the cube, the four-dimensional cube is to the cube, just like the cube is to the square, the four-dimensional cube is the four-dimensional convex polycell, there are 8 cubes of the square of the cube, the cube dimension greater than 3 is the promotion of the hypercube and the bi or measure polysome. Celebration of the chop.