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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
and cantellations. Runcinated hexateron Small prismated hexateron (Acronym: spix) (Jonathan Bowers) The vertices of the runcinated 5-simplex can be most
Runcinated_5-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 enneazetton Small prismated enneazetton (Acronym: spene) (Jonathan Bowers) The Cartesian coordinates of the vertices of the runcinated 8-simplex
Runcinated_8-simplexes
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
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
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
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
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
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