## ::Tesseract

### ::concepts

-cell::space    Cells::coxeter    Regular::parallel    Geometry::regular    Align::title    Cubes::center

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A net of a tesseract.

In geometry, the tesseract is the four-dimensional analog of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubical cells. The tesseract is one of the six convex regular 4-polytopes.

The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid,<ref>Matila Ghyka, The geometry of Art and Life (1977), p.68</ref> 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".<ref>E. L. Elte, The Semiregular Polytopes of the Hyperspaces, (1912)</ref>

According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες{{#invoke:Category handler|main}} (téssereis aktines or "four rays"), referring to the four lines from each vertex to other vertices.<ref>http://www.oed.com/view/Entry/199669?redirectedFrom=tesseract#eid</ref> In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract".

Tesseract sections
Intro   Geometry    Image gallery    Tessellation    Related uniform polytopes   In popular culture  Notes   References    External links

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