This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309442 #11 Oct 27 2019 11:24:06 %S A309442 5,4,2,3,5,3 %N A309442 Minimum number of colors needed to color the cells of the six regular convex polychora such that no two cells with a common face share the same color (in the order 5-cell, 8-cell, 16-cell, 24-cell, 120-cell, 600-cell). %C A309442 Here, cells are 3-dimensional polyhedra, and faces are 2-dimensional polygons. %C A309442 The sequence is the 4-dimensional analog of A244951. %C A309442 The sequence is also the minimum number of colors needed to color the vertices of the six regular convex polychora such that no two vertices with a common edge share the same color (in the order 5-cell, 16-cell, 8-cell, 24-cell, 600-cell, 120-cell). %e A309442 a(1) = 5, since in the 5-cell, each cell has a common face with every other cell (analogous to the tetrahedron, where each face has a common edge with every other face). %e A309442 a(2) = 4, since in the 8-cell, each cell has a common face with every other cell except its "opposite" cell (analogous to the cube, where each face has a common edge with every other face except its opposite face). %e A309442 a(3) = 2, since the 16-cell's dual graph has no odd-edge cycles (analogous to the octahedron's dual graph having no odd-edge cycles). %e A309442 a(4) = 3, since the 24-cell has at least one 3-color solution, and its dual graph has a 3-vertex subgraph with no 2-color solution. %e A309442 a(5) = 5, since the 120-cell has at least one 5-color solution, and its dual graph has a 30-vertex subgraph with no 4-color solution. %e A309442 a(6) = 3, since the 600-cell has at least one 3-color solution, and its dual graph has a 5-vertex subgraph with no 2-color solution. %Y A309442 Cf. A244951, A273509. %K A309442 nonn,fini,full %O A309442 1,1 %A A309442 _Sangeet Paul_, Aug 03 2019