4D Euclidean space
News Archive
December 2011
This is a perspective projection of the rectified 24-cell, a beautiful uniform polychoron from the 24-cell family. It is bounded by 24 cuboctahedra and 24 cubes.
Interestingly enough, due to the coincidence of the 24-cell with the rectified 16-cell, the rectified 24-cell coincides with the cantellated 16-cell.
17 Dec 2011: Improved the cell count summary tables for the rectified 600-cell, the runcinated 120-cell, and the truncated 600-cell. Used polyhedron icons instead of their verbose names in column headings so that the tables are not overly wide.
1 Dec 2011: The polytope of the month for December is up!
November 2011
This month's polytope is the truncated 16-cell. It is a simple member of the tesseract family of uniform polychora, and the direct 4D analogue of the truncated octahedron. Whereas the truncated octahedron is bounded by 6 squares and 8 hexagons, the truncated 16-cell is bounded by 8 octahedra and 16 truncated tetrahedra.
As a bonus, we have included two animations of the truncated 16-cell rotating through 4D space. Check it out!
9 Nov 2011:
Added explanations to the great rhombicuboctahedron and great rhombicosidodecahedron pages of why the commonly-encountered names “truncated cuboctahedron” and “truncated icosidodecahedron” are wrong.
3 Nov 2011:
Re-touched renderings of the 120-cell: brighten the colors, and reduce clutter by using transparent ridges instead of edges for the structure projections.
1 Nov 2011:
The Polytope of the Month for November is up!
October 2011
This month's polytope is the runcitruncated 5-cell, another cute member of the sweet and simple 5-cell family of 4D uniform polytopes. It is bounded by 5 truncated tetrahedra and 5 cuboctahedra, with the gaps in-between filled in by triangular prisms and hexagonal prisms. Full Cartesian coordinates are provided for your reference.
14 Oct 2011:
The Polytope of the Month for October is up! Sorry for the late update.
Added 5D coordinates for the 5-cell uniform polytopes—these are much nicer than the projected 4D coordinates.
Reduced edge radius in the projections of the omnitruncated 5-cell. They should look nicer now.
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