4D Euclidean space
News Archive
Sep 2024
This month we present another 4D Catalan polychoron, this time from the tesseract family:
This is the rhombipyramidal hecatonenneacontadichoron, the dual of the runcitruncated tesseract. It is bounded by 192 skew rhombic pyramids, 480 polygons, 368 edges, and 80 vertices. Find out more about this pretty polychoron on the rhombipyramidal hecatonenneacontadichoron page!
Full algebraic coordinates are given, as usual.
3 Sep 2024:
The Polytope of the Month for September is finally up!
Aug 2024
This month, we return to the 4D Catalan polychora and introduce this tesseract lookalike:
This is the triangular antitegmatic icosachoron, the dual of the runcinated 5-cell. It is bounded by 20 triangular trapezohedra, 60 rhombuses, 70 edges, and 30 vertices. Although its vertex-centered projection resembles the vertex-centered projection of the tesseract, the two are different shapes with different structures.
Notably, it is one of the few 4D Catalans that have transitive polygons and equal edge lengths, which is rare. Nonetheless, the edges are of two kinds: those where 3 cells meet, and those where 4 cells meet.
Learn more on the triangular antitegmatic icosachoron page! As usual, full Cartesian coordinates are provided.
1 Aug 2024:
The Polytope of the Month for August is up!
Jul 2024
This month, we introduce the deltoidal hexecontahedron:
This Catalan solid is the dual of the rhombicosidodecahedron, and has a surface bounded by 60 kite-shaped faces, along with 60 short edges and 60 long edges, and 62 vertices. Learn more on the deltoidal hexecontahedron page!
As is customary, full algebraic coordinates are available.
2 Jul 2024:
The Polytope of the Month for July is up!
26 Jul 2024:
Minor update: added some missing cross-links to the 4D Catalans.
