A385024 Number of face-connected components of tetragonal disphenoidal cells in the tetragonal disphenoidal honeycomb up to translation, rotation, and reflection.

1, 1, 2, 5, 14, 47, 172, 691, 2881, 12449, 54782, 244992, 1107240, 5050360, 23202236, 107269382, 498622480, 2328953312, 10924738869

Offset

1,3

Comments

These are "free polyforms" because rotation and reflection are allowed.

The tetragonal disphenoidal honeycomb is the dual of the bitruncated cubic honeycomb.

Links

Table of n, a(n) for n=1..19.

Bert Dobbelaere, Peter Kagey, Drake Thomas, and Andrés R. Vindas-Meléndez, Building with Blocks: Enumerating Polyforms on Tilings, arXiv:2602.23301 [math.CO], 2026. See p. 9.

Peter Kagey, Animation illustrating a(5)=14.

Wikipedia, Bitruncated cubic honeycomb

Wikipedia, Tetragonal disphenoid 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: A149903 A149904 A287888 * A115276 A343664 A327702

Adjacent sequences: A385021 A385022 A385023 * A385025 A385026 A385027

Keyword

nonn,hard,more

Author

Peter Kagey and Bert Dobbelaere, Jun 15 2025

Status

approved