A385271 Number of face-connected components of square pyramidal cells in the hexakis cubic honeycomb up to translation, rotation, and reflection of the honeycomb.

1, 1, 2, 3, 9, 17, 60, 166, 606, 2106, 8046, 30801, 122442, 491539, 2007571, 8272122, 34408439, 144084776, 607112043, 2571118048, 10938419260, 46720437135

Offset

0,3

Comments

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

The "hexakis cubic honeycomb" is also called the "pyramidille" and is dual to the truncated cubic honeycomb.

The square pyramidal cells are similar to the convex hull of (0,0,0), (2,0,0), (0,2,0) (2,2,0), and (1,1,1).

Links

Table of n, a(n) for n=0..21.

Peter Kagey, Animation illustrating the a(5)=17 connected 5-cell components.

Wikipedia, Architectonic and catoptric tessellation

Wikipedia, Tetragonal disphenoid honeycomb, see section "Hexakis cubic 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: A302164 A295965 A034467 * A234646 A065965 A296052

Adjacent sequences: A385268 A385269 A385270 * A385272 A385273 A385274

Keyword

nonn,hard,more

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Status

approved