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  • Runcinated 7-simplexes

    • seven-dimensional geometry, a runcinated 7-simplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-simplex. There are 8

    Runcinated 7-simplexes

    Runcinated 7-simplexes

    Runcinated_7-simplexes

  • Runcinated 5-simplexes

    • and cantellations. Runcinated hexateron Small prismated hexateron (Acronym: spix) (Jonathan Bowers) The vertices of the runcinated 5-simplex can be most

    Runcinated 5-simplexes

    Runcinated 5-simplexes

    Runcinated_5-simplexes

  • Runcinated 6-simplexes

    • even k due to symmetrically-ringed Coxeter-Dynkin diagram. The runcinated 6-simplexes are in a set of 35 uniform 6-polytopes based on the [3,3,3,3,3]

    Runcinated 6-simplexes

    Runcinated 6-simplexes

    Runcinated_6-simplexes

  • Runcinated 8-simplexes

    • Runcinated enneazetton Small prismated enneazetton (Acronym: spene) (Jonathan Bowers) The Cartesian coordinates of the vertices of the runcinated 8-simplex

    Runcinated 8-simplexes

    Runcinated 8-simplexes

    Runcinated_8-simplexes

  • Uniform 7-polytope

    • Seven-dimensional geometric object

    convex regular 7-polytopes: {3,3,3,3,3,3} - 7-simplex {4,3,3,3,3,3} - 7-cube {3,3,3,3,3,4} - 7-orthoplex There are no nonconvex regular 7-polytopes. The

    Uniform 7-polytope

    Uniform 7-polytope

    Uniform_7-polytope

  • Stericated 5-simplexes

    • cross-section of the stericated hexateron with a 4-dimensional hyperplane is a runcinated 5-cell. This cross-section divides the stericated hexateron into two pentachoral

    Stericated 5-simplexes

    Stericated 5-simplexes

    Stericated_5-simplexes

  • Rectified 5-cell

    • Uniform polychoron

    series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (tetrahedrons and octahedrons in the case of the rectified

    Rectified 5-cell

    Rectified 5-cell

    Rectified_5-cell

  • Truncated 5-cell

    • polyhedron, {4,6|3}, is similarly related to the square faces of the runcinated 5-cell. The disphenoidal 30-cell is the dual of the bitruncated 5-cell

    Truncated 5-cell

    Truncated 5-cell

    Truncated_5-cell

  • 120-cell

    • Four-dimensional analog of the dodecahedron

    unless it is all 5 vertices. It is impossible to rotate two concentric 4-simplexes with respect to each other such that some, but not all, of their vertices

    120-cell

    120-cell

    120-cell

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