8-cell

English Tesseract right|thumb|A Schlegel diagram of an 8-cell Etymology From en 8 cell. Pronunciation en /ˈeɪtˌsɛl/ Noun en geometry A four-dimensional polytope, analogous to a cube, whose eight bounding facets are cubes; a tesseract. en Higher-dimensional geometry en 1988 Klaus Mainzer Symmetries of Nature: A Handbook for Philosophy of Nature and Science https://books.google.com.au/books?id=rqzaQo6CaA0C&pg=PA159&dq=%228-cell%22%7C%228-cells%22+%22dimension%22+OR+%22dimensional%22&hl=en&sa=X&ved=0ahUKEwiL_PL8kerMAhXEJJQKHf6eAgoQ6AEIWjAL#v=onepage&q=%228-cell%22%7C%228-cells%22%20%22dimension%22%20OR%20%22dimensional%22&f=false 159 1996 According to this table the tetrahedron corresponds to the 5-cell, the cube to the 8-cell ("hypercube"), the octahedron to the 16-cell, the dodecahedron to the 120-cell and the icosahedron to the 600-cell. The 24-cell is an additional body in four-dimensional space which is dual to itself. en 1996 w:John Milnor Growing Up in the Old Fine Hall w:Hugo Rossi Prospects in Mathematics: Invited Talks on the Occasion of the 250th Anniversary of Princeton University https://books.google.com.au/books?id=7IkB7zRT4oIC&pg=PA6&dq=%228-cell%22%7C%228-cells%22+%22dimension%22+OR+%22dimensional%22&hl=en&sa=X&ved=0ahUKEwj72O2ivOrMAhWiPKYKHVh5CLU4ZBDoAQgqMAM#v=onepage&q=%228-cell%22%7C%228-cells%22%20%22dimension%22%20OR%20%22dimensional%22&f=false 6 Similarly in dimension eight there is the quaternionic projective plane which we can think of as a 4-sphere with an 8-cell attached, and in dimension sixteen there is a Cayley projective plane which has similar properties. en 1997 J. François Gabriel Beyond the Cube: The Architecture of Space Frames and Polyhedra 412 https://books.google.com.au/books?id=FkM0945nFV8C&pg=PA412&dq=%228-cell%22%7C%228-cells%22+%22dimension%22+OR+%22dimensional%22&hl=en&sa=X&ved=0ahUKEwiL_PL8kerMAhXEJJQKHf6eAgoQ6AEIQTAG#v=onepage&q=%228-cell%22%7C%228-cells%22%20%22dimension%22%20OR%20%22dimensional%22&f=false Of these nine, five are finite structures in Euclidean space and include the simplex, {3,3,3} (or 5-cell), the four-dimensional cube {4,3,3} (or 8-cell) and its dual {3,3,4} (or 16-cell), and the 120-cell {5,3,3} and its dual {3,3,5} (or 600-cell). Synonyms 4-dimensional polytope analogous to a cube en 4-cube, en hypercube (or 4-dimensional hypercube), en cubic prism, en octachoron, en octahedroid, en tesseract Hypernyms polytope analogous to a cube en hypercube Translations four-dimensional polytope Esperanto: eo okĉelo Italian: it ipertetraedro m, it tesseratto m, it ipercubo quadridimensionale m Japanese: ja 正八胞体 せいはちほうたい, seihachihōtai Korean: ko 정팔포체(正八胞體) Polish: pl tesserakt m en Mathematics Shapes