A cell is a three-dimensional object that is part of a higher-dimensional object, such as a polychoron. A cell is related to higher-dimensional objects in the way that a face, or two-dimensional polygon, is related to 3-dimensional objects. For example, a cell is to a 4-dimensional polytope, or polychoron, what a face is to a 3-dimensional polytope, or polyhedron. Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ... In geometry, a four-dimensional polytope is sometimes called a polychoron (plural: polychora) (from Greek poly meaning many and choros meaning room or space), 4-polytope, or polyhedroid. ... Wiktionary has a definition of: Polygon For other use please see Polygon (disambiguation) A polygon (literally many angle, see Wiktionary for the etymology) is a closed planar path composed of a finite number of sequential line segments. ... In geometry polytope means, first, the generalization to any dimension of polygon in two dimensions, and polyhedron in three dimensions. ... In mathematics, there are three related meanings of the term polyhedron: in the traditional meaning it is a 3-dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. ...
The boundary of the 24-cell is composed of 24 octahedral cells with six meeting at each vertex.
Two of the octahedral cells, the nearest and farther from the viewer along the W-axis, project onto an octahedron whose vertices lie at the center of the cuboctahedron's square faces.
Surrounding this central octahedron lie the projections of 16 other cells, having 8 pairs that each project to one of the 8 volumes lying between a triangular face of the central octahedron and the closest triangular face of the cuboctahedron.
Feeds |
Contact