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

0,3

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

Table of n, a(n) for n=0..17.

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).

Sequence in context: A103275 A278209 A195732 * A038987 A142957 A191058

Adjacent sequences: A385274 A385275 A385276 * A385278 A385279 A385280

Keyword

nonn,more,hard

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Status

approved