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).
LINKS
Wikipedia, Architectonic and catoptric tessellation
Wikipedia, Rhombic dodecahedral honeycomb, see section "Rhombic pyramidal 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).
KEYWORD
nonn,hard,more
AUTHOR
Peter Kagey and Bert Dobbelaere, Jun 25 2025
STATUS
approved
