A038168 -id:A038168 - cp's OEIS frontend

A038173 Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice and reflections.

Original entry on oeis.org

1, 1, 4, 20, 131, 1211, 12734, 144158, 1687737, 20196788, 245366931, 3016835487

Offset: 1

Achim Flammenkamp

This extends earlier work of Torsten Sillke (torsten.sillke(AT)lhsystems.com).

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

Cf. A000162, A038119 (for simple-cubic lattice), A038168-A038174, A300812 (refined by number of contacts).

33rd row of A366766.

a(10) from George Sicherman, Jul 24 2012
a(11) from Joerg Arndt and Márk Péter Légrádi, Apr 30 2023
a(12) from Bert Dobbelaere, Jun 26 2025

A038181 Number of "connected animals" formed from n 4-gon or 6-gon connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

Original entry on oeis.org

1, 2, 6, 35, 251, 2602, 30900, 400818, 5401599, 74617105, 1047497078, 14888851869

Offset: 1

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

These are "free polyforms" consisting of face-connected polyhedral cells in the bitruncated cubic honeycomb. - Peter Kagey, Jun 23 2025

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.
M. Owen, Splatts
T. Sillke, Notations for polyspheres
Index entries for sequences related to b.c.c. lattice
Wikipedia, Bitruncated cubic honeycomb

Cf. A000162, A038119, A038168-A038174, A038180, A038386.

More terms from Achim Flammenkamp
Definition corrected by Fred Bayer, Aug 11 2010
More terms from Mark Owen, Oct 11 2013

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

A038171 Number of "connected animals" formed from n 6-gon connected truncated octahedra (or corner connected cubes) in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

Original entry on oeis.org

1, 1, 3, 12, 61, 407, 3226, 28335, 262091, 2501168, 24328920, 239931556

Offset: 1

Achim Flammenkamp

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

Cf. A000162, A038119, A038168-A038174.

35th row of A366766.

a(10) and a(11) from Joerg Arndt and Márk Péter Légrádi, Apr 30 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

A038170 Number of "connected animals" formed from n 6-gon connected truncated octahedra (or corner-connected cubes) in the b.c.c. lattice, allowing translation and rotations of the lattice.

Original entry on oeis.org

1, 1, 3, 14, 88, 686, 5966, 54722, 516454, 4970445, 48527372, 479314799

Offset: 1

Achim Flammenkamp

nonn

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

Cf. A000162, A038119, A038168-A038174.

a(11) and a(12) from Joerg Arndt and Márk Péter Légrádi, May 02 2023

A038172 Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice.

Original entry on oeis.org

1, 1, 5, 28, 225, 2274, 24955, 286143, 3367443, 40358811, 490598186

Offset: 1

Achim Flammenkamp

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.
G. L. Sicherman, Catalogue of Polyrhons
T. Sillke, Notations for polyspheres
Index entries for sequences related to f.c.c. lattice

Cf. A000162, A038119, A038168-A038174.

This extends earlier work of Torsten Sillke (TORSTEN.SILLKE(AT)LHSYSTEMS.COM). Added the 10th term.

a(11) from Joerg Arndt and Márk Péter Légrádi, Apr 30 2023

A038180 Number of "connected animals" formed from n square- or hexagon-connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice.

Original entry on oeis.org

1, 2, 6, 44, 394, 4680, 59361, 789303, 10742595, 148921162, 2093400002, 29769338104

Offset: 1

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

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

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

Corrected and extended by Achim Flammenkamp
Definition corrected by Fred Bayer, Aug 11 2010
More terms from Mark Owen, Oct 11 2013

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

A276272 Number of polytets with n cells, distinguishing mirror images.

Original entry on oeis.org

1, 1, 1, 4, 10

Offset: 1

George Sicherman, Aug 26 2016

A polytet or polytetrahedron is a solid formed by joining platonic tetrahedra face to face.

			a(4) = 4 because four cells can be grouped around a common edge, or have each of three attached to the fourth, or be joined in series; and the last case has distinct mirror images.

G. L. Sicherman, Catalogue of Polytets

Cf. A119602 (number of polytetrahedra allowing edge connections as well as face connections), A038168.

cp's OEIS Frontend

A038173 Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice and reflections.

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A038181 Number of "connected animals" formed from n 4-gon or 6-gon connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

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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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A038171 Number of "connected animals" formed from n 6-gon connected truncated octahedra (or corner connected cubes) in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

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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.

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A038170 Number of "connected animals" formed from n 6-gon connected truncated octahedra (or corner-connected cubes) in the b.c.c. lattice, allowing translation and rotations of the lattice.

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A038172 Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice.

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A038180 Number of "connected animals" formed from n square- or hexagon-connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice.

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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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A276272 Number of polytets with n cells, distinguishing mirror images.

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