runcinate การใช้

• This construction is based on facets of the runcinated 9-orthoplex.
• The 40 triangular faces of the runcinated 5-cell can be seen as removed.
• The 384 triangular faces of the runcinated 24-cell can be seen as removed.
• Hence, the runcinated tesseract may be thought of as the 4-dimensional analogue of the rhombicuboctahedron.
• The rhombicuboctahedron is also constructed from the cube or the octahedron in an analogous way to the runcinated tesseract.
• The maximal cross-section of the runcinated 5-cell with a 3-dimensional hyperplane is a cuboctahedron.
• These square faces can be seen on the runcinated 5-cell, using all 60 edges and 20 vertices.
• These square faces can be seen on the runcinated 24-cell, using all 576 edges and 288 vertices.
• The tetrahedron-first orthographic projection of the runcinated 5-cell into 3-dimensional space has a cuboctahedral envelope.
• The maximal cross-section of the stericated hexateron with a 4-dimensional hyperplane is a runcinated 5-cell.
• This cross-section divides the runcinated 5-cell into two tetrahedral hypercupolae consisting of 5 tetrahedra and 10 triangular prisms each.
• The dual regular skew polyhedron, { 4, 8 | 3 }, is similarly related to the square faces of the runcinated 24-cell.
• The rhombicuboctahedron is used in three uniform space-filling tessellations : the cantellated cubic honeycomb, the runcitruncated cubic honeycomb, and the runcinated alternated cubic honeycomb.
• The vertices can be seen in 3 hyperplanes, with the 10 vertices rectified 5-cells cells on opposite sides, and 20 vertices of a runcinated 5-cell passing through the center.
• In six-dimensional geometry, a "'runcinated 5-simplex "'is a convex uniform 5-polytope with 3rd order truncations ( Runcination ) of the regular 5-simplex.
• In seven-dimensional geometry, a "'runcinated 7-simplex "'is a convex uniform 7-polytope with 3rd order truncations ( runcination ) of the regular 7-simplex.
• In eight-dimensional geometry, a "'runcinated 8-simplex "'is a convex uniform 8-polytope with 3rd order truncations ( runcination ) of the regular 8-simplex.
• In six-dimensional geometry, a "'runcinated 6-cube "'is a convex uniform 6-polytope with 3rd order truncations ( runcination ) of the regular 6-cube.
• In six-dimensional geometry, a "'runcinated 6-orthplex "'is a convex uniform 6-polytope with 3rd order truncations ( runcination ) of the regular 6-orthoplex.
• In seven-dimensional geometry, a "'runcinated 7-cube "'is a convex uniform 7-polytope with 3rd order truncations ( runcination ) of the regular 7-cube.