16-cell

English right|thumb|A 16-cell (Schlegel diagram) Etymology From en 16 cell. Pronunciation en /sɪksˈtiːnˌsɛl/ en en-us-16-cell.ogg US Noun en geometry A four-dimensional polytope, analogous to an octahedron, whose sixteen bounding facets are tetrahedra. en Higher-dimensional geometry en 1995 Harold Scott Macdonald Coxeter Paper Three: Two Aspects Of The Regular 24-Cell In Four Dimensions F. Arthur Sherk Kaleidoscopes: Selected Writings of H.S.M. Coxeter https://books.google.com.au/books?id=fUm5Mwfx8rAC&pg=PA32&dq=%2216-cell%22%7C%2216-cells%22&hl=en&sa=X&ved=0ahUKEwi1wv_l_eXMAhVqpIMKHQFoAcQ4ZBDoAQiEATAW#v=onepage&q=%2216-cell%22%7C%2216-cells%22&f=false 32 The remaining 8, as before, are the vertices of the complementary 16-cell (see Figure 9). In Figure 7, these 8 points have been blackened, but not joined, because the 16-cell has longer edges; diameters of octahedral facets of the 24-cell. en 2002 Gabor Toth Glimpses of Algebra and Geometry 2nd https://books.google.com.au/books?id=U7sSXFIHcl0C&pg=PA385&dq=%2216-cell%22%7C%2216-cells%22&hl=en&sa=X&ved=0ahUKEwjHrd2p7OXMAhXH7YMKHZhEAW8Q6AEIiQEwEQ#v=onepage&q=%2216-cell%22%7C%2216-cells%22&f=false 385 This polytope has 16 tetrahedral cells, and for this reason it is called the 16-cell.The 16-cell has 24 edges that are the diagonals of the 24 square faces of the hypercube. (Since we are selecting alternate vertices of the hypercube, we only get one diagonal for each square face.) en 2012 John Barnes Gems of Geometry 2nd https://books.google.com.au/books?id=7YCUBUd-4BQC&pg=PA76&dq=%2216-cell%22%7C%2216-cells%22&hl=en&sa=X&ved=0ahUKEwjHrd2p7OXMAhXH7YMKHZhEAW8Q6AEIRjAG#v=onepage&q=%2216-cell%22%7C%2216-cells%22&f=false 76 We will now consider the dual 16-cell. In some ways the 16-cell is a bit easier because it has fewer vertices and edges. But on the other hand the hypercube is perhaps easier to understand intuitively because we can readily (perhaps) see the various cubes of which it is composed. Synonyms 4-dimensional polytope analogous to an octahedron en 4-orthoplex, en 4-demicube, en 4-hemicube, en demihypercube, en demitesseract, en hexadecachoron, en hexadecahedroid Translations four-dimensional object Esperanto: eo deksesĉelo Greek: el υπεροκτάεδρο n, el ορθόπλεξη f Italian: it 16-cella f, it 4-ortoplesso m, it ipertetraedro m, it esadecacoro m Japanese: ja 正十六胞体 せいじゅうろくほうたい, seijūrokuhōtai Korean: ko 정십육포체(正十六胞體) Russian: ru шестнадцатиячейник en Mathematics Shapes