This cross-section divides the runcinated 5-cell into two tetrahedral hypercupolae consisting of 5 tetrahedra and 10 triangular prisms each.
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The dual regular skew polyhedron, { 4, 8 | 3 }, is similarly related to the square faces of the runcinated 24-cell.
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The rhombicuboctahedron is used in three uniform space-filling tessellations : the cantellated cubic honeycomb, the runcitruncated cubic honeycomb, and the runcinated alternated cubic honeycomb.
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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.
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In six-dimensional geometry, a "'runcinated 5-simplex "'is a convex uniform 5-polytope with 3rd order truncations ( Runcination ) of the regular 5-simplex.
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In seven-dimensional geometry, a "'runcinated 7-simplex "'is a convex uniform 7-polytope with 3rd order truncations ( runcination ) of the regular 7-simplex.
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In eight-dimensional geometry, a "'runcinated 8-simplex "'is a convex uniform 8-polytope with 3rd order truncations ( runcination ) of the regular 8-simplex.
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In six-dimensional geometry, a "'runcinated 6-cube "'is a convex uniform 6-polytope with 3rd order truncations ( runcination ) of the regular 6-cube.
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In six-dimensional geometry, a "'runcinated 6-orthplex "'is a convex uniform 6-polytope with 3rd order truncations ( runcination ) of the regular 6-orthoplex.
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In seven-dimensional geometry, a "'runcinated 7-cube "'is a convex uniform 7-polytope with 3rd order truncations ( runcination ) of the regular 7-cube.
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