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 A121273 #14 Feb 16 2025 08:33:02 %S A121273 1,3,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %T A121273 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, %U A121273 1,1,1,1,1,1,1,1,1,1,1 %N A121273 Number of different n-dimensional convex regular polytopes that can tile n-dimensional space. %C A121273 The only n-dimensional convex regular polytope that can tile n-dimensional space for all n>4 is the n-hypercube %H A121273 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Space-FillingPolyhedron.html">Space-Filling Polyhedron</a>. %H A121273 Wikipedia, <a href="http://en.wikipedia.org/wiki/List_of_regular_polytopes">Regular Polytopes</a>. %H A121273 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2. %F A121273 a(n)=3 for n = 2 & 4. a(n)=1 for all other n. %e A121273 a(2)=3 because the plane can be tiled by equilateral triangles, squares or regular hexagons. a(3)=1 since the only platonic solid that can tile 3-dimensional space is the cube. a(4)=3 because the 4-dimensional space can be tiled by hypercubes (tesseracts), hyperoctahedra or 24-cell polytopes. %Y A121273 Cf. A053016, A060296. %K A121273 nonn %O A121273 1,2 %A A121273 _Sergio Pimentel_, Aug 23 2006