A038172 -id:A038172 - cp's OEIS frontend

A038174 Number of "polyspheres", or "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the f.c.c. lattice, allowing translation and rotations of the lattice, reflections and 180 deg. rotations about a 3-fold symmetry axis of the lattice.

Original entry on oeis.org

1, 1, 4, 25, 210, 2209, 24651, 284768, 3360995, 40328652, 490455189

Offset: 1

Achim Flammenkamp, Torsten Sillke (TORSTEN.SILLKE(AT)LHSYSTEMS.COM)

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.
Ishino Keiichiro, Polysphere, Puzzle will be played, 2008.
T. Sillke, Notations for polyspheres
Index entries for sequences related to f.c.c. lattice

Cf. A000162, A038119, A038168, A038169, A038170, A038171, A038172, A038173.

a(9) and a(10) from Achim Flammenkamp Feb 15 1999

a(11) from Ishino Keiichiro's website added by Andrey Zabolotskiy, Mar 03 2023

A038169 Number of "connected animals" formed from n triakis truncated tetrahedra connected along hexagonal faces in the triakis truncated tetrahedral honeycomb, allowing translations, rotations, and reflections of the honeycomb.

Original entry on oeis.org

1, 1, 1, 3, 7, 24, 88, 385, 1713, 8112, 38869, 190128, 938357

Offset: 1

Achim Flammenkamp

Previous name was 'Number of "connected animals" formed from n tricapped truncated tetrahedra in the diamond lattice, allowing translation and rotations of the lattice and reflections.' - Peter Kagey, May 30 2025

A. T. Balaban and Paul von R. Schleyer, "Graph theoretical enumeration of polymantanes", Tetrahedron, (1978), vol. 34, pp. 3599-3609. See Page 3605.

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.
Peter Kagey, Illustration of a(5)=7.
Wikipedia, Triakis truncated tetrahedral honeycomb

Cf. A000162, A038119, A038168, A038170, A038171, A038172, A038173, A038174.

Name changed by Peter Kagey, May 30 2025

cp's OEIS Frontend

A038174 Number of "polyspheres", or "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the f.c.c. lattice, allowing translation and rotations of the lattice, reflections and 180 deg. rotations about a 3-fold symmetry axis of the lattice.

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