5. Tesseract

In geometry, the tesseract is the four-dimensional analog of the cube.

Hypercube is composed of:

8 Cells (or Cubes),  24 Faces,  32 Edges  and  16 Vertices

and it meets the extension of Euler's formula:   

Faces + Vertices = Cells + Edges       

There may be different types of representations; such as this where all edges have the same length:

 

 

Or a central projection:

 

 

In four dimensions, the hypercube is also called tesseract (from the greek τέσσερις ακτίνες or "four beams").

 

A famous example of a tesseract is the Arch of La Défense, a monument located in the modern district of La Défense in Paris. The official name in French is Grande Arche de la Fraternité.

 

 

http://www.mathematische-basteleien.de/hypercube.htm

http://zibalsc.blogspot.fr/2010/12/2-formula-di-eulero-per-i-poliedri.html

http://en.wikipedia.org/wiki/Tesseract