A121273 Number of different n-dimensional convex regular polytopes that can tile n-dimensional space.

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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Comments

The only n-dimensional convex regular polytope that can tile n-dimensional space for all n>4 is the n-hypercube

Links

Table of n, a(n) for n=1..79.

Eric Weisstein's World of Mathematics, Space-Filling Polyhedron.

Wikipedia, Regular Polytopes.

Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.

Formula

a(n)=3 for n = 2 & 4. a(n)=1 for all other n.

Example

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.

Crossrefs

Cf. A053016, A060296.

Sequence in context: A073272 A268442 A175623 * A063065 A324724 A051718

Adjacent sequences: A121270 A121271 A121272 * A121274 A121275 A121276

Keyword

nonn

Author

Sergio Pimentel, Aug 23 2006

Status

approved