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The rhombic triacontahedron is an Archimedean solid, which consists of 30 Rhombuses

image

I need a model like this to be a base for one of my projects.

I thought about creating a solid with 10 hexagons as base and then subdivide it, but I couldn't manage it at the end.

Bálint
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2 Answers2

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This shape can be modeled using Extra Objects addon or in a manual way.

Extra Objects addon has preset accessible for rhombic triacontahedron. You'll need to activate addon in User Preferences, see more on how to activate / install an addon.

With addon enabled, from Shift+A menu find Mesh > Math function > Regular Solid. Then you'll tweak its parameters:

scr of adding mesh

In Last Operator panel load preset:

scr of setting up mesh

Or change parameters for Source, Vertex Truncation and Dual.

To model it manually:

  1. Start with icosphere, 1 subdivision.
  2. Poke faces with Alt+P.. This will create geometry necessary for the middle of rombes.
  3. Select one newly created vertex (from poked ones).
  4. Select similar with Shift+G > Amount of connecting edges. Scale them out along normals a bit.
  5. Select all, convert to quads (Alt+J).

GIF modeling mesh

  1. As resulting faces are non-planar (i.e. not all vertices are located on the same imaginary plane), make them planar using Mesh > Clean-Up > Make Planar Faces with around 4 iterations (thanks to Leon Cheung).
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Mr Zak
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  • well : ) ... I was close : )) – lemon Jul 25 '16 at 16:54
  • For the manual method, actually you can hardly scale to make all quads planar enough in this way. I would suggest Alt J then increase the Max Face Angle parameter, then Mesh > Clean Up > Make Planar Faces, increase the Interations. – Leon Cheung Jul 26 '16 at 04:15
  • @LeonCheung you are right, they are non-planar. I thought about that but for some reason didn't check. Generally, it's still possible to scale those vertices - Make Non-planar will handle with the job, so there won't be non-planar ones under 5 degrees. – Mr Zak Jul 26 '16 at 09:20
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You can start from a dodecahedron to do that.

enter image description here

The dodecahedron is a regular solid given in the 'extra object' addon. It looks like this:

enter image description here

So, starting from it, the idea is to remove each edge which cut each pentagon (do that for all the pentagons):

enter image description here

And replace it by a center, like this:

  • Extrude E, then scale to zero S0

enter image description here

Once done for all faces, you can remove all double and obtain this which is the geometry you want, except that rhombic parts are not flat:

enter image description here

To make them flat, select all the pentagons centers, then scale:

enter image description here

This scaling will be approximative, but now:

Enter edit mode again, select all, then make quad with AltJ:

enter image description here

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lemon
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  • For the first step, you needn't do that for all pentagons, just select all then X -> Limited Dissolve. Another way is selecting one of the diagonale then Shift G > Length, then X > Only Edges & Faces, then select all and F to fill all holes with ngons. – Leon Cheung Jul 26 '16 at 04:28