What is a teseract?

Answer 1

In four dimensional geometry, the tesseract, also called an 8-cell or regular octachoron, is the four-dimensional analog of the cube, which is in turn the three dimensional analog of the square. The tesseract is to the cube as the cube is to the square; or, more formally, the tesseract can be described as a regular convex 4-polytope whose boundary consists of eight cubical cells. WIKIPEDIA The tesseract can be constructed in a number of different ways. As a regular polytope with three cubes folded together around every edge, it has Schläfli symbol {4,3,3}. Constructed as a 4D hyperprism made of two parallel cubes, it can be named as a composite Schläfli symbol {4,3}x{ }. As a duoprism, a Cartesian product of two squares, it can be named by a composite Schläfli symbol {4}x{4}. Since each vertex of a tesseract is adjacent to four edges, the vertex figure of the tesseract is a regular tetrahedron. The dual polytope of the tesseract is called the hexadecachoron, or 16-cell, with Schläfli symbol {3,3,4}. The standard tesseract in Euclidean 4-space is given as the convex hull of the points (±1, ±1, ±1, ±1). That is, it consists of the points: : A tesseract is bounded by eight hyperplanes (xi = ±1). Each pair of non-parallel hyperplanes intersects to form 24 square faces in a tesseract. Three cubes and three squares intersect at each edge. There are four cubes, six squares, and four edges meeting at every vertex. All in all, it consists of 8 cubes, 24 squares, 32 edges, and 16 vertices.