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    4-polytope

    In geometry, a 4-polytope is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces, and cells. Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853. The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb, which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling. Convex 4-polytopes can be cut and unfolded as nets in 3-space. Wikipedia

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  2. en.wikipedia.org

    In geometry, a 4-polytope (sometimes also called a polychoron, [1] polycell, or polyhedroid) is a four-dimensional polytope. [2] [3] It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (), and cells ().Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853.
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  4. en.wikipedia.org

    The tesseract is one of 6 convex regular 4-polytopes. In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope.They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions.. There are six convex and ten star regular 4-polytopes, giving a total of sixteen.
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  6. en.wikipedia.org

    Schlegel diagram for the truncated 120-cell with tetrahedral cells visible Orthographic projection of the truncated 120-cell, in the H 3 Coxeter plane (D 10 symmetry). Only vertices and edges are drawn. In geometry, a uniform 4-polytope (or uniform polychoron) [1] is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
  7. polytope.miraheze.org

    This list of uniform polychora is sorted based on Jonathan Bowers' Polychoron Site. Currently, 2191 uniform polychora are known, plus two infinite families: the polygonal duoprisms and polygonal-antiprismatic prisms. There are also 1411 fissary polychora excluded from the main count.
  8. polytope.net

    Six new uniform polychora were discovered in 2020! The uniform polychoron count jumped to 1855 plus many fissaries. These six discovered are sidditsphit, gidditsphit, setut, getut, pecuexidfap, and pecuexdap - four in the sishi regiment, and the last two in a new regiment with the vertices of the grand antiprism - all in category 20.
  9. polytope.miraheze.org

    Regular convex polychora [edit | edit source]. The regular convex polychora are the 4-dimensional counterparts to the Platonic solids and the regular convex polygons.There are 6 regular convex polychora. Apart from the infinite set of regular convex polygons, there are more regular convex polytopes of rank 4 than of any other rank. They have been known about for a long time; however, due to a ...
  10. www3.mpifr-bonn.mpg.de

    Thus, all regular polychora with centrally symmetric vertex polyhedra - and only those - have equatorial polyhedra, and the latter are always rectifications of regular polyhedra. Such equatorial polyhedra are edge sections of polychora by 3-D planes that pass through their centres and are located either between opposite pairs of cells or vertices.
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