A038181 -id:A038181 - cp's OEIS frontend

A038386 Number of "connected animals" formed from n 4-gon or 6-gon connected truncated octahedra in the b.c.c. lattice, allowing only translation of the lattice.

Original entry on oeis.org

1, 7, 67, 734, 8716, 109070, 1416284, 18903142, 257718235, 3573580367

Offset: 1

Torsten Sillke (TORSTEN.SILLKE(AT)LHSYSTEMS.COM)

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.
T. Sillke, Notations for polyspheres
Index entries for sequences related to b.c.c. lattice

Cf. A000162, A038119, A038168-A038174, A038180, A038181.

More terms from Achim Flammenkamp

Name corrected and a(9)-a(10) from Aaron N. Siegel, May 31 2022

A385028 Number of face-connected components of polyhedral cells in the bisymmetric hendecahedral honeycomb up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 1, 4, 16, 116, 903, 8551

Offset: 0

Peter Kagey, Aug 13 2025

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

A bisymmetric hendecahedron is an 11-sided polyhedron that is similar to the convex hull of (-2,1,-1), (-2,1,1), (-1,-1,0), (0,-1,-1), (0,-1,1), (0,0,-2), (0,0,2), (0,2,0), (1,-1,0), (2,1,-1), and (2,1,1).

			For n = 2, the a(2) = 4 distinct compounds of two bisymmetric hendecahedra correspond to placing the four distinct types of faces (square, kite, rhombus, and triangle) together.

Peter Kagey, Illustration of the a(3)=16 components with three polyhedra.
Wikipedia, Bisymmetric hendecahedron
Jiangmei Wu and Guy Inchbald, Folding Space-Filling Bisymmetric Hendecahedron for a Large-Scale Art Installation, Bridges 2018 Conference Proceedings.
Jiangmei Wu, Synergia (sculpture made from bisymmetric hendecahedra).

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), A385278 (triangular pyramidille).

cp's OEIS Frontend

A038386 Number of "connected animals" formed from n 4-gon or 6-gon connected truncated octahedra in the b.c.c. lattice, allowing only translation of the lattice.

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