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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]
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 25 pages use this file: 120-cell; 16-cell; 24-cell; 4-polytope; 600-cell; Complex polytope; Coxeter element; Coxeter group; Euclidean geometry; Four-dimensional space
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 ...
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.
For example a 16-cell is (1,2) 4 = (1,4,4) 2 = (1,8,24,32,16). There are many possible orthographic projections that can show the cross-polytopes as 2-dimensional graphs. Petrie polygon projections map the points into a regular 2 n -gon or lower order regular polygons.
The regular convex 4-polytopes are the four-dimensional analogues of the Platonic solids in three dimensions and the convex regular polygons in two dimensions. Each convex regular 4-polytope is bounded by a set of 3-dimensional cells which are all Platonic solids of the same type and size.
The 600-cell is the fifth in the sequence of 6 convex regular 4-polytopes (in order of complexity and size at the same radius). [a] It can be deconstructed into twenty-five overlapping instances of its immediate predecessor the 24-cell, [5] as the 24-cell can be deconstructed into three overlapping instances of its predecessor the tesseract (8-cell), and the 8-cell can be deconstructed into ...