5-cell

English right|thumb|A Schlegel diagram of a 5-cell Etymology From en 5 cell. Pronunciation en /ˈfaɪvˌsɛl/ Noun en geometry A four-dimensional polytope, analogous to a tetrahedron, whose five bounding facets are tetrahedra. en Higher-dimensional geometry en 1896 American Journal of Mathematics https://books.google.com.au/books?id=UiBLAAAAYAAJ&q=%225-cell%22%7C%225-cells%22+tetrahedra&dq=%225-cell%22%7C%225-cells%22+tetrahedra&hl=en&sa=X&ved=0ahUKEwjs1NaRpubMAhUMyoMKHeKzAIcQ6AEIzgIwOQ 181 In every vertex of the 5-cell, 8-cell and 120-cell there are 4 concurring edges; in every vertex of the 24-cell, 8 edges. en 1988 Unnamed L. A. Sidorov Confuguration Michiel Hazewinkel Encyclopaedia of Mathematics: An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’ Volume 2: C, page 309 For example, a 5-cell is bounded by five three-dimensional tetrahedra, an 8-cell by eight cubes, etc., the 5-cell and the 24-cell being duals of each other (the points correspond to spaces and lines to planes). en 2007 Steven R. Lay Convex Sets and Their Applications 230 https://books.google.com.au/books?id=U9eOPjmaH90C&pg=PA230&dq=%225-cell%22%7C%225-cells%22+tetrahedra&hl=en&sa=X&ved=0ahUKEwjs1NaRpubMAhUMyoMKHeKzAIcQ6AEIUTAK#v=onepage&q=%225-cell%22%7C%225-cells%22%20tetrahedra&f=false If we call a regular polytope with m facets an m-cell, then in E4 we have the 5-cell with tetrahedral facets (the simplex), the 8-cell with cubic facets (the hypercube), the 16-cell with tetrahedral facets (the regular cross-polytope), the 24-cell with octahedral facets, the 120-cell with dodecahedral facets, and the 600-cell with tetrahedral facets. en 2008 Tony Robbin Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought 16 https://books.google.com.au/books?id=TRABcDhRNYcC&pg=PA16&dq=%225-cell%22%7C%225-cells%22+%224-simplex%22&hl=en&sa=X&ved=0ahUKEwiukbnprubMAhUC74MKHc8iCpoQ6AEIVTAL#v=onepage&q=%225-cell%22%7C%225-cells%22%20%224-simplex%22&f=false Later in the same document, President Hall listed all of the university's four-dimensional models: four Brill models—the 5-cell, 8-cell, 16-cell, and 24-cell—along with seven spun glass models by T. P. Hall that "illustrated rotations." Synonyms 4-dimensional polytope analogous to a tetrahedron en 4-simplex, en pentachoron, en pentahedroid, en pentatope, en tetrahedral pyramid Translations four-dimensional polytope analogous to a tetrahedron Esperanto: eo kvinĉelo Italian: it 5-cella f, it ipertetraedro m, it pentacoro m Japanese: ja 正五胞体 せいごほうたい, seigohōtai Korean: ko 정오포체(正五胞體) Polish: pl pięciościan czterowymiarowy m en Mathematics Shapes