A385277 Number of face-connected components of triangular prismatic cells in the triangular prismatic honeycomb up to translation, rotation, and reflection of the honeycomb.

1, 1, 2, 3, 11, 30, 137, 606, 3243, 17681, 101718, 593931, 3532385, 21220273, 128680158, 785895888, 4830179751, 29847223514

Offset: 0

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Keywords

• nonn
• more
• hard

Comments

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

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

Links

• Peter Kagey, Animation illustrating the a(5)=30 connected 5-cell components.
• Wikipedia, Triangular 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), A385267 (half pyramidille), A385268 (oblate cubille), A385269 (quarter cubille), A385270 (elongated dodecahedral), A385271 (hexakis cubic), A385272 (phyllic disphenoidal), A385273 (quarter oblate octahedrille), A385274 (rhombic pyramidal), A385275 (square quarter pyramidille), A385276 (trapezo-rhombic dodecahedral), A385277 (triangular prismatic).