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

Author

Peter Kagey and Bert Dobbelaere, Jun 15 2025

Keywords

• nonn
• hard
• more

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

• 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).