A385026 Number of face-connected components of hexagonal prism cells in the hexagonal prismatic honeycomb up to translation, rotation, and reflection of the honeycomb.

1, 2, 5, 20, 89, 569, 4002, 31899, 266736, 2315811, 20531349, 184927106, 1684835315

Offset

1,2

Comments

These are "free polyforms" because they are counted up to rotation and reflection.

The hexagonal prismatic honeycomb is the dual of the triangular prismatic honeycomb.

Links

Table of n, a(n) for n=1..13.

Peter Kagey, Animation illustrating a(4)=20.

Wikipedia, Triangular prismatic honeycomb. (See section "Hexagonal prismatic honeycomb.")

Crossrefs

Cf. A038119 (cubic), A038173 (rhombic dodecahedral), A038181 (truncated octahedral), A343909 (tetrahedral-octahedral), A365654 (square bipyramidal), A384254 (rectified cubic), A384274 (quarter cubic), A384754 (omnitruncated cubic), A385024 (tetragonal disphenoidal), A385025 (gyrobifastigium), A385026 (hexagonal prismatic), A385027 (triakis truncated tetrahedral).

Sequence in context: A262172 A258830 A002484 * A280102 A366452 A277686

Adjacent sequences: A385023 A385024 A385025 * A385027 A385028 A385029

Keyword

nonn,hard,more

Author

Peter Kagey and Bert Dobbelaere, Jun 15 2025

Status

approved