24-cell

English right|thumb|A Schlegel diagram of a 24-cell Etymology From en 24 cell. Pronunciation en /twɛntiˈfoʊɹˌsɛl/ Noun 24-cell en geometry A four-dimensional polytope whose twenty-four bounding facets are octahedra and which has no three-dimensional analogue. en Higher-dimensional geometry en 1995 w:Harold Scott Macdonald Coxeter Paper Three: Two Aspects of the Regular 24-Cell in Four Dimensions F. Arthur Sherk; Peter McMullen; Anthony C. Thompson; Asia Iviċ Weiss Kaleidoscopes: Selected Writings of H.S.M. Coxeter https://books.google.com.au/books?id=fUm5Mwfx8rAC&pg=PA25&dq=%2224-cell%22%7C%2224-cells%22&hl=en&sa=X&ved=0ahUKEwj1_uOi2urMAhXh36YKHSlzDrYQ6AEIQzAG#v=onepage&q=%2224-cell%22%7C%2224-cells%22&f=false 25 The octagonal projection of the regular 24-cell {3,4,3} reveals that the 24 vertices of this 4-dimensional polytope can be distributed as 16 + 8: the 16 vertices of the 4-cube γ4 = {4,3,3} and the 8 vertices of its dual, the 16-cell β4 = {3,3,4}. This view of the 24-cell is less well-known than the dodecagonal projection, in which the β4 appears as two squares of different sizes joined by 8 equilateral triangles. 2002, T. Robbin, Formian for art and mathematics, G. A. R. Parke, P. Disney (editors), Space Structures 5, Proceedings of the 5th International Conference on Space Structures, Volume 1, page 445, One more example of a four dimensional tessellation is given using the 24-cell, see Fig 2. en 2002 Gabor Toth Glimpses of Algebra and Geometry 2nd https://books.google.com.au/books?id=U7sSXFIHcl0C&pg=PA385&dq=%2224-cell%22%7C%2224-cells%22&hl=en&sa=X&ved=0ahUKEwjczNKF5erMAhUEoJQKHcoRAC84ZBDoAQhGMAg#v=onepage&q=%2224-cell%22%7C%2224-cells%22&f=false 385 The regular polytope with Schläfli symbol {3,4,3}, the so-called 24-cell, can be obtained from the 16-cell as follows. The vertices of the 24-cell are the midpoints of the 24 edges of the 16-cell. Synonyms 4-dimensional polytope with 24 octahedral facets en hyper-diamond, en icositetrachoron, en octacube, en octaplex, en polyoctahedron, Translations four-dimensional polytope Esperanto: eo dudekkvarĉelo Finnish: fi 24-solu Japanese: ja 正二十四胞体 せいにじゅうしほうたい, seinijūshihōtai Korean: ko 정이십사포체(正二十四胞體) en Mathematics Shapes