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I'm trying to make a model of the first atomic bomb's high explosive lens configuration:

Example from Wikipedia

The shape is a truncated icosahedron composed of extruded octagons and pentagons.

Modeling a single solid truncated icosahedron is easy — there are lots of tutorials out there under "how to model a soccer ball" (make an icosphere, apply a single subsurf to it, tweak the center of the vertices a little).

But I'm struggling to see how I can turn something like that into a model that is composed of the 32 separate 3D octagons and pentagons.

So far I've tried making a truncated icosahedron, extruding it, deleting the all of the shapes except one pair of inner/outer octagons, connecting their edges manually (since extrude won't for such a complex shape)... which is a very slow and tricky process (it's a lot of vertices/edges to wade through for each shape).

Is there a better way that I am missing? If I had one octagon and one pentagon, would it be then easy to have them tile around the sphere in this way? (I haven't been able to manage it with Array or Mirror; the angles seem just a little too eccentric for the transformation defaults).

Any suggestions would be appreciated.

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    $\begingroup$ Related, How can I create a hollow sphere with regularly spaced holes?. $\endgroup$ – iKlsR Jan 8 '14 at 19:14
  • $\begingroup$ Creating the initial shape (and others) is even easier, enable the Regular Solids addon then you can Add->Mesh->Solids->Archimeadean->Truncated Icosahedron $\endgroup$ – sambler Jan 9 '14 at 13:46
  • $\begingroup$ @sambler — I tried this, but I found the faces came out pretty ugly that way. $\endgroup$ – nucleon Jan 13 '14 at 0:31
  • $\begingroup$ Well the edit mode view might look a little messy - the extra edges are because it's all quads and tris - no ngons. Edge split will still split in the same place and the rendered result will look the same. $\endgroup$ – sambler Jan 13 '14 at 6:37
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I accomplished this. I have removed some of the facets to show the inner side.

bomb

This is how:

  1. Make a football (as you said, subsurf an icosahedron, dissolve all vertices on middle and edges).
  2. Add the edge split modifier with split angle 1. This will make each ngon (pentagon and hexagon) separate from its neigbours.
  3. Apply the modifier.
  4. Go into edit mode and select all faces.
  5. Extrude all faces but right click directly. This will make them double but select all faces that will form the outer shell.
  6. Scale out the selected faces.
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DISCLAIMER: I use Rhinoceros.

I also attempted to model the explosive lenses of the bomb, and after painstakingly modelling a truncated icosahedron, modelling a sphere broken into segments with a pattern of a truncated icosahedron (I made a soccer ball), then looked at some additional reference photos of the lenses, and realised that I was completely off.

enter image description here

I realised that the arrangement of the explosive lenses was not a common (32 sided) truncated icosahedron. The lenses of the actual bomb are all pentagons of equal area, which means that they're easier to manufacture and work with, but finding the side lengths of the pentagons without rotational symmetry was a headache. I eventually solved the problem using algebra, and used those measurements to construct a solid with flat sides, before making a sphere with the same surface pattern. I then hollowed out a proportionally sized sphere, finishing the 72 segments of the sphere.

enter image description here

If anyone wants a copy of my 3d model, email me with your preferred file type

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