cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 16 results. Next

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

Original entry on oeis.org

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

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 15 2025

Keywords

Comments

These are "free polyforms" because rotation and reflection are allowed.
The tetragonal disphenoidal honeycomb is the dual of the bitruncated cubic honeycomb.

Links

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).

A385026 Number of face-connected components of hexagonal prism cells in the hexagonal prismatic honeycomb up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 2, 5, 20, 89, 569, 4002, 31899, 266736, 2315811, 20531349, 184927106, 1684835315
Offset: 1

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 15 2025

Keywords

Comments

These are "free polyforms" because they are counted up to rotation and reflection.
The hexagonal prismatic honeycomb is the dual of the triangular prismatic honeycomb.

Links

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).

A385027 Number of face-connected components of triakis truncated tetrahedral cells in the triakis truncated tetrahedral honeycomb up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 2, 8, 71, 793, 11486, 177746, 2876127, 47667178, 804571359, 13773260905
Offset: 1

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 15 2025

Keywords

Comments

According to Wikipedia, the triakis truncated tetrahedral honeycomb "is the Voronoi tessellation of the carbon atoms in diamond."

Links

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 Number of face-connected components of half pyramidille cells in the half pyramidille up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 1, 3, 4, 13, 29, 106, 331, 1222, 4390, 16588, 62865, 243217, 947711, 3732800, 14801687, 59103268, 237305379, 957738244, 3882631356, 15804400624
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

Comments

The half pyramidille is the dual to the cantitruncated tetrahedral-octahedral honeycomb (also known as the runcicantic cubic honeycomb) which consists of truncated cuboctahedra, truncated cubes and truncated tetrahedra.
Each cell is similar to the convex hull of (0,0,0), (2,0,0), (2,2,0), and (1,1,1).

Links

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).

A385268 Number of face-connected components of oblate cubille cells in the oblate cubille up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 1, 1, 3, 7, 24, 93, 427, 2043, 10412, 54072, 287121, 1543567, 8393603, 46040030, 254484780, 1415837030, 7922633039
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

Comments

These are "free polyforms" because two connected components are considered to be the same if one can be rotated or reflected to match the other.
Each cell is 1/4 of a rhombic dodecahedron, and is similar to the convex hull of (-1,1,1), (0,0,0), (0,0,2), (0,2,0), (1,-1,1), (1,1,-1), (1,1,1), and (2,0,0).
The "oblate cubille" is also called the "trigonal trapezohedral honeycomb."

Links

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).

A385269 Number of face-connected components of quarter cubille cells in the quarter cubille up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 1, 2, 4, 18, 67, 374, 2063, 12482, 76835, 486375, 3119695, 20275051, 133031450, 880300617, 5866722906
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

Comments

These are "free polyforms" because they are counted up to rotation and reflection.
The quarter cubille is the dual to the runcic cubic honeycomb (equivalently, the cantellated tetrahedral-octahedral honeycomb) which consists of rhombicuboctahedra, cubes, and tetrahedra.
Each cell is similar to the convex hull of (0,2,2), (2,0,2), (2,2,0), (2,2,2), and (1,1,1).

Links

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).

A385270 Number of face-connected components of elongated dodecahedral cells in the elongated dodecahedral honeycomb up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 1, 2, 8, 48, 362, 3530, 37861, 431383, 5059338, 60577228, 736054522, 9050344941, 112374575115
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

Comments

These are "free polyforms" because they are counted up to rotation and reflection.
The symmetry group of the elongated dodecahedron is D_4h, which is prismatic symmetry of order 16.

Links

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).

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

Original entry on oeis.org

1, 1, 2, 3, 9, 17, 60, 166, 606, 2106, 8046, 30801, 122442, 491539, 2007571, 8272122, 34408439, 144084776, 607112043, 2571118048, 10938419260, 46720437135
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Keywords

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

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).

A385272 Number of face-connected components of phyllic disphenoidal cells in the phyllic disphenoidal honeycomb up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 1, 2, 4, 13, 38, 141, 515, 2043, 8176, 33706, 140471, 593705, 2531933, 10893811, 47202599, 205843902, 902644191, 3977976135, 17609163491
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Keywords

Comments

These are "free polyforms" because they are counted up to rotation and reflection.
The "phyllic disphenoidal honeycomb" is also called the "eighth pyramidille," and its dual is the omnitruncated cubic honeycomb.
The phyllic disphenoidal cells are similar to the convex hull of (0,0,0), (1,0,0), (1,1,0), and (1,1,1).

Links

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).

A385273 Number of face-connected components of polyhedral cells in the quarter oblate octahedrille up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 1, 2, 6, 24, 114, 647, 3883, 24605, 159837, 1060450, 7137627, 48624639, 334475495, 2319909330, 16205238283
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Keywords

Comments

These are "free polyforms" because they are counted up to rotation and reflection.
The quarter oblate octahedrille is dual to the cantellated cubic honeycomb.
The cells of the quarter oblate octahedrille are similar to the convex hull of (0,0,0), (1,0,0), (0, 1, 0), (1,1,1), and (1,1,-1).

Links

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).
Showing 1-10 of 16 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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