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Tesseract

Tesseract 8-cell 4-cube Type Convex regular 4-polytope Schläfli symbol {4,3,3} t0,3{4,3,2} or {4,3}×{ } t0,2{4,2,4} or {4}×{4} t0,2,3{4,2,2} or {4}×{ }×{ } t0,1,2,3{2,2,2} or { }×{ }×{ }×{ } Coxeter diagram Cells 8 (4.4.4) Faces 24 {4} Edges 32 Vertices 16 Vertex figure Tetrahedron Petrie polygon octagon Coxeter group C4, Dual 16-cell Properties convex, isogonal, isotoxal, isohedral Uniform index 10 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, 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".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 t?sse?e?? a?t??e? (téssereis aktines or "four rays"), referring to the four lines from each vertex to other vertices. In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract". ^ Matila Ghyka, The geometry of Art and Life (1977), p.68 ^ E. L. Elte, The Semiregular Polytopes of the Hyperspaces, (1912) ^ http://www.oed.com/view/Entry/199669?redirectedFrom=tesseract#eid
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