0,3

These are "free polyforms" because they are counted up to rotation and reflection.

The dual of the square quarter pyramidille is the runcitruncated cubic honeycomb.

Each irregular pyramidal cell is similar to the convex hull of (0,0,0), (0,0,1), (0,1,0), (0,1,1), and (1,1,1).

Peter Kagey, Animation illustrating the a(4)=26 connected 4-cell components.

Wikipedia, Architectonic and catoptric tessellation

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: A058258 A376970 A215397 * A359974 A214309 A005646

Adjacent sequences: A385272 A385273 A385274 * A385276 A385277 A385278

nonn,hard,more

Peter Kagey and Bert Dobbelaere, Jun 25 2025

approved