Concept
24-cell honeycomb
Concepts associés (14)
Uniform 5-polytope
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope facets. The complete set of convex uniform 5-polytopes has not been determined, but many can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter diagrams.
16-cell honeycomb
In four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {3,3,4,3}, and constructed by a 4-dimensional packing of 16-cell facets, three around every face. Its dual is the 24-cell honeycomb. Its vertex figure is a 24-cell. The vertex arrangement is called the B4, D4, or F4 lattice. Hexadecachoric tetracomb/honeycomb Demitesseractic tetracomb/honeycomb Vertices can be placed at all integer coordinates (i,j,k,l), such that the sum of the coordinates is even.
5-cell honeycomb
In four-dimensional Euclidean geometry, the 4-simplex honeycomb, 5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation honeycomb. It is composed of 5-cells and rectified 5-cells facets in a ratio of 1:1. Cells of the vertex figure are ten tetrahedrons and 20 triangular prisms, corresponding to the ten 5-cells and 20 rectified 5-cells that meet at each vertex.
Tesseractic honeycomb
In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol {4,3,3,4}, and constructed by a 4-dimensional packing of tesseract facets. Its vertex figure is a 16-cell. Two tesseracts meet at each cubic cell, four meet at each square face, eight meet on each edge, and sixteen meet at each vertex. It is an analog of the square tiling, {4,4}, of the plane and the cubic honeycomb, {4,3,4}, of 3-space.
Snub 24-cell honeycomb
In four-dimensional Euclidean geometry, the snub 24-cell honeycomb, or snub icositetrachoric honeycomb is a uniform space-filling tessellation (or honeycomb) by snub 24-cells, 16-cells, and 5-cells. It was discovered by Thorold Gosset with his 1900 paper of semiregular polytopes. It is not semiregular by Gosset's definition of regular facets, but all of its cells (ridges) are regular, either tetrahedra or icosahedra. It can be seen as an alternation of a truncated 24-cell honeycomb, and can be represented by Schläfli symbol s{3,4,3,3}, s{31,1,1,1}, and 3 other snub constructions.
Truncated 24-cell honeycomb
In four-dimensional Euclidean geometry, the truncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a truncation of the regular 24-cell honeycomb, containing tesseract and truncated 24-cell cells. It has a uniform alternation, called the snub 24-cell honeycomb. It is a snub from the construction. This truncated 24-cell has Schläfli symbol t{31,1,1,1}, and its snub is represented as s{31,1,1,1}.
Hexadécachore
L'hexadécachore est, en géométrie, un 4-polytope régulier convexe, c'est-à-dire un polytope à 4 dimensions à la fois régulier et convexe. Il est constitué de 16 cellules tétraédriques. L'hexadécachore est l'hyperoctaèdre de dimension 4. Son dual est le tesseract (ou hypercube). Il pave l'espace euclidien à quatre dimensions.
Complex polytope
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. A complex polytope may be understood as a collection of complex points, lines, planes, and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on. Precise definitions exist only for the regular complex polytopes, which are configurations.
Icositétrachore
L'icositétrachore, ou « 24-cellules » est un 4-polytope régulier convexe. Il est spécifique à la dimension 4 dans le sens où il ne possède aucun équivalent dans une autre dimension. On le dénomme aussi « 24-cellules », « icositétratope », ou « hypergranatoèdre ». On peut définir un icositétrachore dans au moyen des sommets de coordonnées , ainsi que ceux obtenus en permutant ces coordonnées. Ils sont au nombre de 24.
Polytope régulier
droite|vignette|Le dodécaèdre régulier, un des cinq solides platoniciens. En mathématiques, plus précisément en géométrie ou encore en géométrie euclidienne, un polytope régulier est une figure de géométrie présentant un grand nombre de symétries. En dimension deux, on trouve par exemple le triangle équilatéral, le carré, les pentagone et hexagone réguliers, etc. En dimension trois se rangent parmi les polytopes réguliers le cube, le dodécaèdre régulier (ci-contre), tous les solides platoniciens.