| 1. | This construction is based on facets of the runcinated 9-orthoplex.
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| 2. | The 40 triangular faces of the runcinated 5-cell can be seen as removed.
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| 3. | The 384 triangular faces of the runcinated 24-cell can be seen as removed.
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| 4. | Hence, the runcinated tesseract may be thought of as the 4-dimensional analogue of the rhombicuboctahedron.
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| 5. | The rhombicuboctahedron is also constructed from the cube or the octahedron in an analogous way to the runcinated tesseract.
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| 6. | The maximal cross-section of the runcinated 5-cell with a 3-dimensional hyperplane is a cuboctahedron.
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| 7. | These square faces can be seen on the runcinated 5-cell, using all 60 edges and 20 vertices.
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| 8. | These square faces can be seen on the runcinated 24-cell, using all 576 edges and 288 vertices.
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| 9. | The tetrahedron-first orthographic projection of the runcinated 5-cell into 3-dimensional space has a cuboctahedral envelope.
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| 10. | The maximal cross-section of the stericated hexateron with a 4-dimensional hyperplane is a runcinated 5-cell.
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