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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 ...
In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra .
These cells might also play a critical role in complex object recognition within the visual processing areas of the cortex. [3] Relative to other species, the larger cell size and complexity of pyramidal neurons, along with certain patterns of cellular organization and function, correlates with the evolution of human cognition. [22]
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.
Order-5 5-cell honeycomb; 120-cell honeycomb; Order-5 tesseractic honeycomb; Order-4 120-cell honeycomb; Order-5 120-cell honeycomb; Order-4 24-cell honeycomb; Cubic honeycomb honeycomb; Small stellated 120-cell honeycomb; Pentagrammic-order 600-cell honeycomb; Order-5 icosahedral 120-cell honeycomb; Great 120-cell honeycomb
The 5-orthoplex of the cross polytope family, {3,3,3,4}, with 10 vertices, 40 edges, 80 faces (each a triangle), 80 cells (each a tetrahedron), and 32 hypercells (each a 5-cell). An important uniform 5-polytope is the 5-demicube, h{4,3,3,3} has half the vertices of the 5-cube (16), bounded by alternating 5-cell and 16-cell hypercells. The ...
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The 5-cell (4-simplex) is self-dual with 5 vertices and 5 tetrahedral cells. If a polytope has the same number of vertices as facets, of edges as ridges, and so forth, and the same connectivities, then the dual figure will be similar to the original and the polytope is self-dual. Some common self-dual polytopes include: