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A385274
Number of face-connected components of rhombic pyramidal cells in the rhombic pyramidal honeycomb up to translation, rotation, and reflection of the honeycomb.
13
1, 1, 2, 4, 14, 43, 197, 850, 4154, 20371, 103405, 530355, 2760533, 14499363, 76842876, 410164367, 2203491401, 11903591737
OFFSET
0,3
COMMENTS
These are "free polyforms" because they are counted up to rotation and reflection.
The "rhombic pyramidal honeycomb" is also called the "half oblate octahedrille" and is dual to the cantic cubic honeycomb, which is also called the "truncated tetraoctahedrille" or the "truncated tetrahedral-octahedral honeycomb"
The rhombic pyramidal cells are similar to the convex hull of (0,0,0), (1,1,1), (1,1,-1), (0,2,0), and (2,0,0).
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).
Sequence in context: A169982 A367101 A243323 * A128750 A047152 A007866
KEYWORD
nonn,hard,more
AUTHOR
Peter Kagey and Bert Dobbelaere, Jun 25 2025
STATUS
approved