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Wednesday, October 31, 2012

Tesseract - A Four Dimensional Cube

In Marvel movie The Avengers, it is stated that the Tesseract contains an unimaginable power and can be used as weapon of mass destruction if the power can be unlocked. Well, the tesseract that i'm refering to is not in the movie but rather the one in field of geometry.

Tesseract from the movie The Avengers
According to wikipedia, a tesseract is a four dimensional analog of the cube and sometimes is called 8-cell, regular octahoron or cubic prism. Tesseract is a four dimensional hypercube, (cube with dimension higher than 3) and first proposed by Charles Howard Hinton, a British mathematician in the 19th century. 

A tesseract image in Schlegel diagram.
A tesseract can be unfolded into 8 cubes in 3D space, the same as a cube unfolded 6 squares in 2D surface. The image below shows how a tesseract can be build from 1 dimensional space until the first cube projection in 4 dimensional space.

How to draw a tesseract from a single point ie one dimension.

There are other types of tesseract for example truncated tesseract and rectified tesseract in which they have different Schlafli Symbol and Schlegel diagram.  The existence of higher dimension is by far an abstract concept and none have observed these higher dimensions. Nonetheless, the mathematics suggests the possibility and therefore could exist in this vast universe.


p/s: I read somewhere in which lower dimensional object couldn't possibly see the higher dimension but the higher dimensional object can definitely see the lower one. Not sure how this implicates the existence of higher deity though. 

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