A385270 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

Table of n, a(n) for n=0..13.

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).

Sequence in context: A054726 A003576 A225042 * A326887 A095989 A177388

Adjacent sequences: A385267 A385268 A385269 * A385271 A385272 A385273

KEYWORD

nonn,hard,more

AUTHOR

Peter Kagey and Bert Dobbelaere, Jun 23 2025

STATUS

approved