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All four dimensions are necessary for strength and stability. [3] Other models of hauora have been designed. For example, in 1997, Lewis Moeau, iwi leader and later cultural advisor for the Prime Minister suggested that a fifth dimension, whenua (connection with the land), be added to the original model. [4]
Sommerville also considers the case of a simplex in four dimensions: [2] "The Schlegel diagram of simplex in S 4 is a tetrahedron divided into four tetrahedra." More generally, a polytope in n-dimensions has a Schlegel diagram constructed by a perspective projection viewed from a point outside of the polytope, above the center of a facet.
In geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere. History on four-dimensional groups
The following other wikis use this file: Usage on ar.wikipedia.org ثلاثوني الأضلاع; رباعي الأبعاد; Usage on bn.wikipedia.org
Every graph is the line graph of some hypergraph, but, given a fixed edge size k, not every graph is a line graph of some k-uniform hypergraph. A main problem is to characterize those that are, for each k ≥ 3. A hypergraph is linear if each pair of hyperedges intersects in at most one vertex. Every graph is the line graph, not only of some ...
The convex regular 4-polytopes can be ordered by size as a measure of 4-dimensional content (hypervolume) for the same radius. Each greater polytope in the sequence is rounder than its predecessor, enclosing more content [5] within the same radius. The 4-simplex (5-cell) is the limit smallest case, and the 120-cell is the largest.
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 C 5, hypertetrahedron, pentachoron, [1] pentatope, pentahedroid, [2] tetrahedral pyramid, or 4-simplex (Coxeter's polytope), [3] the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three ...
Cells 4-faces 5-faces 6-faces ... Skeleton graph Hemitesseract {4,3,3}/2 {4,3,3} 4: 4: 12: 16: 8: 0: ... A skew apeirogon in two dimensions forms a zig-zag line in ...