Draw a truncated octahedron packing in 3D

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Consider a truncated octahedron composed by

  • 24 vertices (4×6)
  • 14 faces (contain 6 squares and 8 hexagons)
  • 36 edges (4×6+6×82=36).

This truncated octahedron can pack and tessellate the 3-dimensional-space like this.

Question: What are the available methods to draw this in Mathematica? (My attempt was that I showed such packing is possible and prepared this figure [not using Mathematica..].)

enter image description here

wonderich

Posted 2020-02-16T00:30:07.650

Reputation: 603

Answers

3

g = PolyhedronData["TruncatedOctahedron", "Faces", "Polygon"];

u = {2, 0, Sqrt[2]};
v = {0, 2, -Sqrt[2]};
w = {0, 2, Sqrt[2]};
Graphics3D[
 Table[
  {Opacity[0.7], RandomChoice[{Orange, Blue}],
   GeometricTransformation[g, 
    TranslationTransform[i u + j v + k w]]},
  {i, 3}, {j, 3}, {k, 3}]]

enter image description here

David G. Stork

Posted 2020-02-16T00:30:07.650

Reputation: 31 784

1thanks +1, but I am not sure the object you draw can do packing/tessellation in 3D...? – wonderich – 2020-02-16T07:01:51.663

maybe of interests too https://mathematica.stackexchange.com/questions/214858

– wonderich – 2020-02-18T03:48:09.213