A385270 Number of face-connected components of elongated dodecahedral cells in the elongated dodecahedral honeycomb up to translation, rotation, and reflection of the honeycomb.

1, 1, 2, 8, 48, 362, 3530, 37861, 431383, 5059338, 60577228, 736054522, 9050344941, 112374575115

Offset: 0

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

• nonn
• hard
• more

Comments

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

The symmetry group of the elongated dodecahedron is D_4h, which is prismatic symmetry of order 16.

Links

• Peter Kagey, Animation illustrating the a(4)=48 connected 4-cell components.
• Wikipedia, Elongated dodecahedron
• Wikipedia, Parallelohedron

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).