0,3

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).

Peter Kagey, Animation illustrating the a(5)=38 connected 5-cell components.

Wikipedia, Architectonic and catoptric tessellation

Wikipedia, Tetragonal disphenoid honeycomb, see section "Phyllic disphenoidal honeycomb."

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: A268698 A174604 A148253 * A392392 A148254 A163137

Adjacent sequences: A385269 A385270 A385271 * A385273 A385274 A385275

nonn,hard,more

Peter Kagey and Bert Dobbelaere, Jun 25 2025

approved