Concept

5-cell honeycomb

Related concepts (9)
Stericated 5-simplexes
In five-dimensional geometry, a stericated 5-simplex is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-simplex. There are six unique sterications of the 5-simplex, including permutations of truncations, cantellations, and runcinations. The simplest stericated 5-simplex is also called an expanded 5-simplex, with the first and last nodes ringed, for being constructible by an expansion operation applied to the regular 5-simplex.
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}.
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.
24-cell honeycomb
In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells. It can be represented by Schläfli symbol {3,4,3,3}. The dual tessellation by regular 16-cell honeycomb has Schläfli symbol {3,3,4,3}. Together with the tesseractic honeycomb (or 4-cubic honeycomb) these are the only regular tessellations of Euclidean 4-space. The 24-cell honeycomb can be constructed as the Voronoi tessellation of the D4 or F4 root lattice.
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.
Omnitruncated simplectic honeycomb
In geometry an omnitruncated simplectic honeycomb or omnitruncated n-simplex honeycomb is an n-dimensional uniform tessellation, based on the symmetry of the affine Coxeter group. Each is composed of omnitruncated simplex facets. The vertex figure for each is an irregular n-simplex. The facets of an omnitruncated simplectic honeycomb are called permutahedra and can be positioned in n+1 space with integral coordinates, permutations of the whole numbers (0,1,..,n). The (2n-1)-simplex honeycombs can be project
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.
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.
5-cell
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is the 4-simplex (Coxeter's polytope), the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions. The 5-cell is a 4-dimensional pyramid with a tetrahedral base and four tetrahedral sides.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.