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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.
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]
There are 5 fundamental mirror symmetry point group families in 4-dimensions: A 4 = , B 4 = , D 4 = , F 4 = , H 4 = . [7] There are also 3 prismatic groups A 3 A 1 = , B 3 A 1 = , H 3 A 1 = , and duoprismatic groups: I 2 (p)×I 2 (q) = . Each group defined by a Goursat tetrahedron fundamental domain bounded by mirror planes.
Net. In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called a C 120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hecatonicosachoron, dodecacontachoron [1] and hecatonicosahedroid.
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 Mayan calendar’s 819-day cycle has confounded scholars for decades, but new research shows how it matches up to planetary cycles over a 45-year span
Net. In four-dimensional geometry, the 24-cell is the convex regular 4-polytope [1] (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}. It is also called C 24, or the icositetrachoron, [2] octaplex (short for "octahedral complex"), icosatetrahedroid, [3] octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells.
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