A385267 Number of face-connected components of half pyramidille cells in the half pyramidille up to translation, rotation, and reflection of the honeycomb.

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

Offset: 0

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

• nonn
• hard
• more

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

• Peter Kagey, Animation illustrating the a(4) = 13 connected components consisting of 4 cells.
• Wikipedia, Architectonic and catoptric tessellation
• Wikipedia, Tetrahedral-octahedral honeycomb (see subsection "Runcicantic cubic 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), 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).