## Sunday, July 17, 2016

### 10 facts about Tesseract cube

1. The tesseract is a four dimensional cube. the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes.

2. The word tesseract was coined and first used in 1888 by British mathematician Charles Howard Hinton in his book A New Era of Thought. Hinton was also famous for his set of colored cubes that he claimed could be used to help people visualize the fourth dimension.

3. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube (although this last term can also mean a polycube made of four cubes). It is the four-dimensional hypercube, or 4-cube as a part of the dimensional family of hypercubes or "measure polytopes".

4. The number of vertices doubles with every dimension: the segment has 2 of them, the square 4, the cube 8, and the tesseract has 16.

5. In addition to 16 vertices, the tesseract has 32 edges, 24 squares, and 8 cubes - all in 1 tesseract.

6. In Madeleine L'Engle's novel A Wrinkle in Time, the characters in the story travel through time and space using tesseracts. The book actually uses the idea of a tesseract to represent a fifth dimension rather than a four-dimensional object (and also uses the word "tesser" to refer to movement from one three dimensional space/world to another).

7. In the science fiction novel Factoring Humanity by Robert J. Sawyer, a tesseract is used by humans on Earth to enter the fourth dimension and contact another civilization on a planet orbiting the star Alpha Centauri A. The hypercube initially exists as a series of connected 3-dimensional cubes, which represent a hypercube that has been unfolded. Refolding the cube in a certain specific manner causes the reformation of the hypercube in 4 dimensions.

8. In John Mighton's play, Half Life, one of the characters (an aging mathematician) builds a tesseract (or rather, the projection of a tesseract) out of popsicle sticks. In the Season 1 episode "Rampage" of the television crime drama NUMB3RS, main character mathematician Charlie Eppes discovers a popsicle-stick tesseract (projection) he built as a boy.

9. If you are bored with 3D Rubik's cube, you can try your hands on Rubik's tesseract like shown in this video

10. Mathematically, "time" is not "the fourth dimension"; "space time" is a particular physical model, but in mathematics, 4-dimensional Euclidean space is simply the set of all ordered 4-tuples (a,b,c,d)(a,b,c,d) with a,b,c,da,b,c,d real numbers, satisfying certain axioms. Time doesn't enter into it.  Arturo Magidin's comment at math.stackexchange.com

References:

4. The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics by Clifford A. Pickover

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